This is an academic research by apply R statistics analysis to an agency A of an existing betting consultancy firm A. According to the Dixon and Pope (2004)1 Kindly refer to 24th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References, due to business confidential and privacy I am also using agency A and firm A in this paper. The purpose of the anaysis is measure the staking model of the firm A. For more sample which using R for Soccer Betting see http://rpubs.com/englianhu. Here is the references of rmarkdown and An Introduction to R Markdown. You are welcome to read the Tony Hirst (2014)2 Kindly refer to 1st paper in Reference for technical research on programming and coding portion for the paper. in 7.4 References if you are getting interest to write a data analysis on Sports-book.
Before we start modelling, we look at the summary of investment return rates.
table 4.1.1 : 5 x 5 : Return of annually investment summary table.3 Kindly refer to the list of colors via Dark yellow with hexadecimal color code #9B870C for plot the stylist table.
\[\Re = \sum_{i=1}^{n}\rho_{i}^{EM}/\sum_{i=1}^{n}\rho_{i}^{BK} \cdots equation\ 4.1.1\]
\(\Re\) is the edge or so call advantage for an investment. The \(\rho_i^{EM}\) is the estimated probabilities which is the calculated by firm A from match 1,2… until \(n\) matches while \(\rho_{i}^{BK}\) is the net/pure probability (real odds) offer by bookmakers after we fit the equation 4.1.2 into equation 4.1.1.
\[\rho_i = P_i^{Lay} / (P_i^{Back} + P_i^{Lay}) \cdots equation\ 4.1.2\]
\(P_i^{Back}\) and \(P_i^{Lay}\) is the backed and layed fair price offer by bookmakers.
We can simply apply equation above to get the value \(\Re\). From the table above we know that the EMPrice calculated by firm A invested at a threshold edge (price greater) 2.20%, 3.19%, 0.64%, 3.87%, 0.54% than the prices offer by bookmakers. There are some description about \(\Re\) on Dixon and Coles (1996)4 Kindly refer to 25th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. The optimal value of \(\rho_{i}\) (rEMProbB) will be calculated based on bootstrapping/resampling method in section 4.3 Kelly Ⓜodel.
Now we look at the result of the soccer matches prior to filter out for further modelling from this section.
table 4.1.2 : 7 x 8 : Summary of betting results.
The table above summarize the stakes and return on soccer matches result. Well, below table list the handicaps placed by firm A on agency A. Due to the Cancelled result is null observation in descrete data modelling and we cannot be count into our model. Here Ifilter out the particular observation from the data from here and now the total observation of the dataset became 41055.
CORRECTION : need to keep the cancelled matches as the “push” to count in the probability of the cancellation betslip as well which is occurred in real life.
table 4.1.3 : 41055 x 66 : Odds price and probabilities sample table.
Above table list a part of sample odds prices and probabilities of soccer match \(i\) while \(n\) indicates the number of soccer matches. We can know the values rEMProbB, netProbB and so forth.
graph 4.1.1 : A sample graph about the relationship between the investmental probabilities -vs- bookmakers’ probabilities.
Graph above shows the probabilities calculated by firm A to back against real probabilities offered by bookmakers over 41055 soccer matches.
I list the handicap below prior to test the coefficient according to the handicap in next section 4.2 Linear Ⓜodel.
table 4.1.4 : 8 x 6 : The handicap in sample data.
From our understanding of staking, the covariates we need to consider should be only odds price since the handicap’s covariate has settled according to different handicap of EMOdds.
Again, I don’t pretend to know the correct Ⓜodel, here I simply apply linear model to retrieve the value of EMOdds derived from stakes. The purpose of measure the edge overcame bookmakers’ vigorish is to know the levarage of the staking activities onto 1 unit edge of odds price by firm A to agency A. By refer to figure 4.4.1, I includes the models which split the pre-match and in-play ito comparison.
When I used to work in 188Bet and Singbet as well as AS3388, we know from the experience which is the odds price of favorite team win will be the standard reference and the draw odds will adjust a little bit while the underdog team will be ignore.
Steven Xu (2013)5 Kindly refer to 16th paper in Reference for industry knowdelege and academic research portion for the paper. has do a case study on the comparison of the efficiency of opening and closing price of NFL and College American Football Leagues and get to know the closing price is more efficient and accurate compare to opening price nowadays compare to years 1980~1990. It might be due to multi-million dollars of stakes from informed traders or smart punters to tune up the closing price to be likelihood.
In order to test the empirical clichés, I used to conduct a research thoroughly through ®γσ, Eng Lian Hu (2016)6 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References, I completed the research on year 2010 but write the thesis in year 2016. and concludes that the opening price of Asian Handicap and also Goal Lines of 29 bookmakers are efficient than mine. However in my later ®γσ, Eng Lian Hu (2014)7 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References applied Kelly staking model where made a return of more than 30% per sesson. Meanwhile, the Dixon and Coles (1996) and Crowder, Dixon, Ledford and Robinson (2001)8 Kindly refer to 27th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has built two models which compare the accuracy of home win, draw and away win. From a normal Poison model reported the home win is more accurate and therefore an add-hoc inflated parameter required in order to increase the accuracy of prediction. You are feel free to learn about the Dixon and Coles (1996) in section 4.4 Poisson Ⓜodel.
Based on table 2.2.1 we know about the net bookies probabilities and EM probabilities, here I simply apply linear regression model9 You can learn from Linear Regression in R (R Tutorial 5.1 to 5.11). You can also refer to Getting Started with Mixed Effect Models in R, A very basic tutorial for performing linear mixed effects analyses and Fitting Linear Mixed-Effects Models using lme4. Otherwise you can read Linear Models with R and somemore details about regression models via Extending the Linear Model with R : Generalized Linear, Mixed Effects and Nonparametric Regression Models. Besides, What statistical analysis should I use? summarise a table for test analysis and data validation. Fit models to data provides examples for application of linear regression and model selection, the main model-fitting commands covered lm (linear models for fixed effects), lme (linear models for mixed effects), glm (generalized linear models), nls (nonlinear least squares), gam (generalized additive models) and also visreg (to visualize model fits). The answer from How to use R anova() results to select best model? eleborates the use of ANOVA and AIC criterion to choose the best fit model. How to Choose the Best Regression Model describes how to find the best regresion model to fit and applicable to the real world. ANOVA - Model Selection summarised a lecture notes in slideshow while Model Selection in R conducts a research on model selection for non-nested linear and polynomial models. and also anova to compare among the models.
shinyapp 4.2.1 : WDW-AH convertion and summary and anova of linear models. Kindly click on regressionApps10 You might select Y response variable and X explanatory variable(s) to measure your model (Refer to Shiny height-weight example for further information about shinyapp for linear models.) or existing models. to use the ShinyApp.
Here I simply attached with a Fixed Odds to Asian Handicap’s calculator which refer to my ex-colleague William Chen’s11 My ex-colleague and best friend in sportsbook industry which known since join sportsbook industry year 2005 —— Telebiz and later Caspo Inc. spreadsheet version 1.1 in year 2006. You can simply input the home win, draw, away win (in decimal format) as well as the overround to get the conversion result from the simple an basic equation.12 Kindly refer to my previous research to know the vigorish / overround.
From the summary of shinyapp 4.2.1, we know the comparison among the models to get the best fitted model.
table 4.2.1 : Application of linear regression models to test the effects on staking.
table 4.2.2A : Best model to test the effects of staking on all soccer matches (includes both pre-match and in-play).
table 4.2.2B : Best model to test the effects of staking on pre-match soccer matches.
table 4.2.2C : Best model to test the effects of staking on in-play soccer matches.
table 4.2.3 : Best model to test the effects of staking soccer matches.
Base on above few tables and also summarised table 4.2.3, we can compare both lm0 and lm0ip + lm0pm and decide that the model lm0ip + lm0pm13 BIC will be primary reference while AIC is the secondary reference. The smallest value is the best model. all = 446,424.83 and mixed = 444,750.45 is the best fit to determine the factors and effects to place stakes for all matches14 mixed InPlay + Pre-match, all observations are 41055 soccer matches which has placed bets.. The timing of InPlay and the stakes amount is the major effects to the return of investment.
John Fingleton & Patrick Waldron (1999) apply Shin’s model and finally conclude suggests that bookmakers in Ireland are infinitely risk-averse and balance their books. The authors cannot distinguish between inside information and operating costs, merely concluding that combined they account for up to 3.7% of turnover while normally Asian bookmakers made less than 1% and a anonymous company has made around 2%. However the revenue or the stakes are farly more than European bookmakers.15 You can refer to my another project Analyse the Finance and Stocks Price of Bookmakers which analysis the financial report of public listed companies and also profitable products’ revenue and profit & loss of anonymous company..
They compare different versions of our model, using data from races in Ireland in 1993. The authors’ empirical results can be summarised as follows:
figure 4.2.1 : Chance of Winning.
Due to the Shin model inside the paper research for the sake of bookmakers and this sportsbook consultancy firm is indeed the informed trading (means smart punters or actuarial hedge fund but not ordinary gambler place bets with luck). Here I think of test our previous data in paper ®γσ, Eng Lian Hu (2016)16 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References which collect the dataset of opening and also closing odds price of 40 bookmakers and 29 among them with Asian Handicap and Goal Line. Meanwhile, there has another research on smart punters (Punters Account Review (Agenda).xlsx) which make million dollars profit from Ladbrokes. You are feel free to browse over the dataset for the paper. and also the anonymous companies’s revenue and P&L to analyse the portion of smart punters among the customers in Analyse the Finance and Stocks Price of Bookmakers. However the betslip of every single bet require to analyse it. The sparkR amd RHadoop as well as noSQL require in order to analyse the multiple millions bets. It is interesting to analyse the threaten of hedge fund17 Kindly refer to 富传奇色彩的博彩狙击公司EM2 to know the history and the threaten of EM2 sportsbook consultancy company to World wide known bankers. since there has a anonymous brand among the brands under Caspo Inc had closed due to a lot of smart punters’ stakes and made loss. Well, here I leave it for future research18 Here I put in 6.2 Future Works. if the dataset is available.
From the papers Niko Marttinen (2001)19 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. and Jeffrey Alan Logan Snyder (2013)20 Kindly refer to 2nd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References both applying Full-Kelly,Half-Kelly and also Quarter-Kelly models which similar with my previous Kelly-Criterion model ®γσ, Eng Lian Hu 201421 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References which had applied it and generates an impressive return. but enhanced. Niko Marttinen (2001) has concludes that the basic Kelly criterion generates the highest returns in long run compare to fractional Kelly models.
To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Edward O. Thorp (2006)22 Kindly refer to 6th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References has proven to work effectively in betting. It was named after an American economist John Kelly (1956)23 Kindly refer to 26th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References and originally designed for information transmission. The Kelly criterion is described below:
figure 4.3.1.1 : Kelly criterion formula.
\[S = \frac{\rho_{EM} \times BK_{Decimal\ odds} - 1} {BK_{HK\ odds}} \cdots equation\ 4.3.1.1\]
Due to HK odds or decimal odds start from range \((0,\infty]\) and return will be \([0,\infty]\), therefore logarithmic function required. For Malay odds \([-1,1]\) no need logarithm. Here I switch from equation 4.3.1.1 to equation 4.3.1.2 as below.
\[log(S) = log(\rho_{EM}) + log(BK_{Decimal\ odds} - 1) - log(BK_{HK\ odds}) \cdots equation\ 4.3.1.2\]
Three important properties, mentioned by Hausch and Ziemba (1994)24 You can refer to Efficiency of Racetrack Betting Markets (2008 Preface Edition) which is 29th paper in Reference for industry knowdelege and academic research portion for the paper. or Chapter 18 Efficiency of Sports and Lottery Betting Markets in FINANCE for further study about Hausch and Ziemba’s researchs. arise when using this criterion to determine a proper stake for each bet:
figure 4.3.1.2 : Example of application Kelly criterion.
The criterion is known to economists and financial theorists by names such as the geometric mean maximizing portfolio strategy, the growth-optimal strategy, the capital growth criterion, etc. We will now show that Kelly betting will maximize the expected log utility for sports-book betting.
table 4.3.1.1 : 5 x 5 : Return of annually investment summary table without cancelled bets.25 the rRates is the mean value of annual return rates which is the return divides by stakes but ommit the cancelled/voided bets to avoind the bias.
The rRates value from table above excludes the Cancelled bets. By refer to equation 4.3.1.2, now we fit the adge value from equation 4.1.1 into it to get the rEMProbB2 and rEMProbL2 with known staked value \(S\)26 Although the result will not be accurate due to the we mention at first, the firm A will not only place bets via only agent A. Let say edge of 0.10 and 0.20 also placed maximum bet HKD40000 but the firm A might placed different amount through other agency based on different edge. However based on the stakes we can reverse the optimal EM Odds. to replace the existing EM value. 27 Initially think of linear modelling and get the mean value, the positive standard deviation value will be counted as edge range and the residuals value will be the different within the stakes across the leagues. It will similar with proportional staking model as states in paper Good and bad properties of the Kelly criterion by MacLean, Thorp and Ziemba (2010) and concludes that the Full-Kelly model is the best model for long run, you can refer to the reference in Kelly Criterion - Part II for further understanding.
\[log(\rho_{EM}) = log(S) + log(BK_{HK\ odds} + 1) - log(BK_{Decimal\ odds}) \cdots equation\ 4.3.1.3\]
Although the Kelly model is very simple, but we need to seperates the staking based on different leagues or time range to make it applicable to real world. I don’t pretend to know the correct model again but guess the applicable model by testing few models and choose the best among them.
We try to apply the equation 4.3.1.3 to get the Kelly stakes for every single soccer match.
Due to there have few reference papers conducting few staking strategics and concludes full Kelly model is the best fit and most profitable along the long term investment, here I try to simuulate the half-Kelly and also quadruple-Kelly, as well as double-Kelly staking model etc and get the optimal weighted control parameter.28 There has a reference paper in section 2 of Application of Kelly Criterion model in Sportsbook Investment has compare few models as well and also provides the pro-and-con of Kelly model in investment. However, Kelly model will be the best across the long term investment. Besides, there have few papers doing research and also critic on the Kelly model in investment in financial market and also betting market (includes the rebates of the credit market as well), PIMCO’s fund manager Bill Gross who manage more than one trillion USD funds applied Kelly model for portfolio, George Soros and Warren Buffet also applied similar theoty or method with Kelly although there has no evidence to proof it. You are feel free to know in later section 4.5 Staking Ⓜodel and Ⓜoney Ⓜanagement. For further details kindly refer to Application of Kelly Criterion model in Sportsbook Investment.
Fractional Kelly models are the weight function for Kelly criterion When we talk about weight function in Kelly model. A Response to Professor Paul A Samuelson’s Objections to Kelly Capital Growth Investing has talk about the investment portfolio and compare the double-Kelly, full-Kelly, half-Kelly, quadruple-Kelly and also proportional betting across different stages of iterations and concludes that the full-Kelly will be the best fit and growth beyond the ages. Well, fractional-Kelly (means double-Kelly, half-Kelly and quadruple-Kelly but not full-Kelly model) models will be elastics and lesser will be more conservative and double-Kelly will be very risky and eventually going to bankcrupt due to the staking leverages ratio is twice of full-Kelly and over the sustainability of capital. and For further details kindly refer to Application of Kelly Criterion model in Sportsbook Investment. Therefore in last basic Kelly we use the full-Kelly within same leagues but due to there has different levels of risk setting across different soccer leagues. Therefore a weight function needed to make the staking strategy flexible, and it is term as Kelly portfolio to diversified the investment.
Now we try to fit a weight function into basic Kelly model to be fractional Kelly model. I try to use log to test the maximum value of weight parameter. You can just simply use \(w = \frac{1}{4}\) or \(log(w) = \frac{1}{2}\) while \(w\) is a vector. Please be mind that the value greater than 1 will be risky since involve leverage and lesser will be more conservative.
\[log(w_{i}) + log(\rho_{i}) \cdots equation\ 4.3.2.1\]
From Niko Marttinen (2001), we can know the full-Kelly generates couple times profit compare to fractional Kelly-models. However there has two points need to be enhanced.
Below Fabián Enrique Moya (2012) also test the fractional Kelly models with diversify money management methods.
table 4.3.2.1 : 177 x 6 : League stakes profiling of firm A year 2011~2015.
Above league risk profile suppose to stores the maximum bet for every single league but I only randomly select 6 leagues as sample. However due to I’ve not yet write a function for real time API29 There are a lot of real time XML odds price and staking softwares similar with 4lowin2 which was states at the begining section in Part I with operators and test the maximum stakes per bet therefore here I reverse the both mean and median value as the baseline stakes for every single league with a certain range of standard deviation for monte carlo simulation in later section.
Basic Fractional Models
Stakes based reversed Kelly models are the application of the parameter from reversion of the stakes where add-on some modified version Kelly models. I tried to adjust the stakes to get the outcome of PL result.
Table 4.3.2.2A : Summary Table of Various Kelly Models (Stakes reversed based models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 0.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-1.0000 | Min. :-3.480000 | Min. :-5568.000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 0.7164 | Min. : 0.6632 | Min. : 0.7101 | Min. : 0.656 | Min. : 1.018 | Min. : 0.8478 | Min. :0.2353 | Min. :0.07552 | Min. : 0.5651 | Min. : 0.4839 | Min. : 0.4062 | Min. : 0.2808 | Min. : 1.018 | Min. : 0.8478 | Min. : 0.6814 | Min. : 0.5262 | Min. : 0.411 | Min. : 0.2758 | Min. : 0.5113 | Min. : 0.5095 | Min. : 0.50 | Min. : 0.50 | Min. : 0.50 | Min. : 0.50 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. : 0.50 | Min. : 0.50 | Min. : 0.04419 | Min. : 0.0186 | Min. : 0.001752 | Min. : 0.00001 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. :-1703.881 | Min. :-1703.877 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-0.81996 | Min. :-0.81996 | Min. :-399.5146 | Min. :-399.5869 | Min. :-99.2718 | Min. :-99.38039 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-204.07878 | Min. :-225.6129 | Min. :-26.03009 | Min. :-31.81324 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00 | Min. :-1.00 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 12.50 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.:-1.0000 | 1st Qu.:-0.040000 | 1st Qu.: -0.780 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 6.5857 | 1st Qu.: 6.6500 | 1st Qu.: 6.4545 | 1st Qu.: 6.513 | 1st Qu.: 5.562 | 1st Qu.: 5.5095 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 3.4912 | 1st Qu.: 3.5105 | 1st Qu.: 2.0090 | 1st Qu.: 2.0105 | 1st Qu.: 5.562 | 1st Qu.: 5.5095 | 1st Qu.: 4.0210 | 1st Qu.: 4.0020 | 1st Qu.: 2.900 | 1st Qu.: 2.8978 | 1st Qu.: 13.1445 | 1st Qu.: 13.1429 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 2.574 | 1st Qu.: 2.575 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 1.42401 | 1st Qu.: 1.3993 | 1st Qu.: 0.162111 | 1st Qu.: 0.15220 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -18.394 | 1st Qu.: -18.402 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -3.9845 | 1st Qu.: -3.9845 | 1st Qu.: -0.4068 | 1st Qu.: -0.44459 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -2.09361 | 1st Qu.: -2.1492 | 1st Qu.: -0.24835 | 1st Qu.: -0.26395 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00 | 1st Qu.:-1.00 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.0000 | Median : 0.000000 | Median : 0.000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 13.3921 | Median : 13.5570 | Median : 13.1134 | Median : 13.274 | Median : 8.005 | Median : 8.1081 | Median :0.7693 | Median :0.76495 | Median : 6.8155 | Median : 6.8944 | Median : 3.6711 | Median : 3.6931 | Median : 8.005 | Median : 8.1081 | Median : 5.7454 | Median : 5.7943 | Median : 4.139 | Median : 4.1400 | Median : 27.3565 | Median : 27.3569 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median :0.51936 | Median :0.51936 | Median : 6.045 | Median : 6.048 | Median : 0.8272 | Median : 0.8439 | Median : 26.00 | Median : 26.00 | Median : 3.05504 | Median : 3.0992 | Median : 0.359275 | Median : 0.37422 | Median : 16.87 | Median : 16.87 | Median : 16.00 | Median : 16.00 | Median : 16.00 | Median : 16.00 | Median :0.6297 | Median :0.6297 | Median : 3.242 | Median : 3.216 | Median : 0.000 | Median : 0.000 | Median : 16.00 | Median : 16.00 | Median : 1.788 | Median : 1.708 | Median : 0.1975 | Median : 0.1781 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00 | Median : 0.00 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.0332 | Mean : 0.001888 | Mean : -0.123 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 20.2975 | Mean : 20.7183 | Mean : 19.8809 | Mean : 20.292 | Mean : 8.766 | Mean : 9.1770 | Mean :0.7622 | Mean :0.75010 | Mean : 10.2006 | Mean : 10.3990 | Mean : 5.3605 | Mean : 5.4523 | Mean : 8.766 | Mean : 9.1770 | Mean : 6.2743 | Mean : 6.4657 | Mean : 4.496 | Mean : 4.5732 | Mean : 42.3180 | Mean : 42.3180 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean :0.51655 | Mean :0.51655 | Mean : 9.582 | Mean : 9.583 | Mean : 1.8106 | Mean : 1.8265 | Mean : 40.53 | Mean : 40.53 | Mean : 4.73391 | Mean : 4.8490 | Mean : 0.562677 | Mean : 0.61187 | Mean : 43.24 | Mean : 43.24 | Mean : 41.40 | Mean : 41.40 | Mean : 41.40 | Mean : 41.40 | Mean :0.5340 | Mean :0.5340 | Mean : 9.781 | Mean : 9.783 | Mean : 1.842 | Mean : 1.858 | Mean : 41.40 | Mean : 41.40 | Mean : 4.833 | Mean : 4.949 | Mean : 0.5742 | Mean : 0.6242 | Mean : 0.926 | Mean : 0.926 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.1994 | Mean : 0.1992 | Mean : 0.0310 | Mean : 0.03177 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.09928 | Mean : 0.1003 | Mean : 0.01157 | Mean : 0.01232 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.0328 | Mean : 0.0329 | Mean : 0.03 | Mean : 0.03 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 50.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.8500 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.080 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 24.3364 | 3rd Qu.: 24.8399 | 3rd Qu.: 23.8376 | 3rd Qu.: 24.332 | 3rd Qu.:10.885 | 3rd Qu.: 11.3964 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.: 12.1869 | 3rd Qu.: 12.4157 | 3rd Qu.: 6.3529 | 3rd Qu.: 6.4489 | 3rd Qu.:10.885 | 3rd Qu.: 11.3964 | 3rd Qu.: 7.7735 | 3rd Qu.: 7.9939 | 3rd Qu.: 5.561 | 3rd Qu.: 5.6439 | 3rd Qu.: 51.1809 | 3rd Qu.: 51.1847 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.: 11.806 | 3rd Qu.: 11.782 | 3rd Qu.: 2.2386 | 3rd Qu.: 2.2458 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 5.69606 | 3rd Qu.: 5.8483 | 3rd Qu.: 0.681064 | 3rd Qu.: 0.74440 | 3rd Qu.: 55.84 | 3rd Qu.: 55.84 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.: 12.458 | 3rd Qu.: 12.439 | 3rd Qu.: 1.980 | 3rd Qu.: 2.021 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 6.160 | 3rd Qu.: 6.223 | 3rd Qu.: 0.7218 | 3rd Qu.: 0.7632 | 3rd Qu.: 21.232 | 3rd Qu.: 21.230 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 4.6300 | 3rd Qu.: 4.6499 | 3rd Qu.: 0.5975 | 3rd Qu.: 0.62808 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 2.36233 | 3rd Qu.: 2.3670 | 3rd Qu.: 0.27408 | 3rd Qu.: 0.28592 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.88 | 3rd Qu.: 0.90 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :1600.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 2.6550 | Max. : 3.040000 | Max. : 4864.000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :838.2473 | Max. :904.5996 | Max. :812.3153 | Max. :876.612 | Max. :69.868 | Max. :111.6521 | Max. :0.9863 | Max. :0.99149 | Max. :406.4039 | Max. :438.5324 | Max. :203.4483 | Max. :219.4924 | Max. :69.868 | Max. :111.6521 | Max. :48.6334 | Max. :72.2019 | Max. :34.213 | Max. :46.6908 | Max. :1703.8836 | Max. :1703.8839 | Max. :1600.00 | Max. :1600.00 | Max. :1600.00 | Max. :1600.00 | Max. :0.91018 | Max. :0.91018 | Max. :399.515 | Max. :399.587 | Max. :99.2718 | Max. :99.3804 | Max. :1600.00 | Max. :1600.00 | Max. :204.07878 | Max. :225.6129 | Max. :26.030094 | Max. :31.81324 | Max. :3186.26 | Max. :3186.26 | Max. :2992.00 | Max. :2992.00 | Max. :2992.00 | Max. :2992.00 | Max. :1.1573 | Max. :1.1573 | Max. :746.925 | Max. :746.915 | Max. :185.388 | Max. :185.372 | Max. :2992.00 | Max. :2992.00 | Max. :337.202 | Max. :334.563 | Max. :38.0031 | Max. :40.2482 | Max. : 1482.379 | Max. : 1482.379 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 0.49844 | Max. : 0.49844 | Max. : 347.5000 | Max. : 347.4951 | Max. : 86.2500 | Max. : 86.24260 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 156.88006 | Max. : 155.6523 | Max. : 17.68057 | Max. : 17.40491 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65 | Max. : 2.65 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :1348 | NA’s :1383 | NA’s :10832 | NA’s :10297 | NA | NA | NA | NA | NA | NA |
table 4.3.2.2A : 41055 x 110 : Summary of Stakes reversed Kelly models year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.2B : 19 x 6 : PL of Stakes based reversed Kelly models year 2011~2015.
Mean Fractional Models
Due to there has no league risk management profile, here I try to use the mean value of stakes on every single league as the baseline.
Table 4.3.2.2C : Summary Table of Various Kelly Models (Stakes Reversed based with Mean Stakes Adjusted Models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.80 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-11.15344 | Min. :-3.480000 | Min. :-829.4804 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 1.355 | Min. : 1.336 | Min. : 1.351 | Min. : 1.332 | Min. : 2.186 | Min. : 2.130 | Min. :0.2353 | Min. :0.07552 | Min. : 0.9472 | Min. : 0.9408 | Min. : 0.7094 | Min. : 0.6746 | Min. : 2.186 | Min. : 2.130 | Min. : 1.516 | Min. : 1.413 | Min. : 1.051 | Min. : 0.9378 | Min. : 1.826 | Min. : 1.827 | Min. : 1.80 | Min. : 1.80 | Min. : 1.80 | Min. : 1.80 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 1.80 | Min. : 1.80 | Min. : 0.1804 | Min. : 0.02953 | Min. :0.002519 | Min. : 0.00001 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. :-293.50 | Min. :-293.53 | Min. :-271.961 | Min. :-271.961 | Min. :-271.961 | Min. :-271.961 | Min. :-0.81996 | Min. :-0.81996 | Min. :-67.7270 | Min. :-67.8834 | Min. :-16.60281 | Min. :-16.83735 | Min. :-271.961 | Min. :-271.961 | Min. :-47.2073 | Min. :-58.6339 | Min. :-8.19431 | Min. :-12.64128 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 24.74 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.57965 | 1st Qu.:-0.040000 | 1st Qu.: -1.0939 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 12.283 | 1st Qu.: 11.969 | 1st Qu.: 12.053 | 1st Qu.: 11.736 | 1st Qu.: 7.465 | 1st Qu.: 7.210 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 6.3027 | 1st Qu.: 6.1502 | 1st Qu.: 3.4194 | 1st Qu.: 3.3464 | 1st Qu.: 7.465 | 1st Qu.: 7.210 | 1st Qu.: 5.445 | 1st Qu.: 5.322 | 1st Qu.: 3.985 | 1st Qu.: 3.9264 | 1st Qu.: 25.875 | 1st Qu.: 25.877 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 5.629 | 1st Qu.: 5.631 | 1st Qu.: 0.683 | 1st Qu.: 0.6385 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 2.7283 | 1st Qu.: 2.59540 | 1st Qu.:0.296708 | 1st Qu.: 0.26185 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -27.71 | 1st Qu.: -27.71 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -6.0601 | 1st Qu.: -6.1016 | 1st Qu.: -0.87215 | 1st Qu.: -0.90198 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -3.1072 | 1st Qu.: -3.1151 | 1st Qu.:-0.35981 | 1st Qu.: -0.37010 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 29.22 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 15.523 | Median : 16.232 | Median : 15.202 | Median : 15.884 | Median : 8.805 | Median : 9.026 | Median :0.7693 | Median :0.76495 | Median : 7.8573 | Median : 8.1836 | Median : 4.1777 | Median : 4.3292 | Median : 8.805 | Median : 9.026 | Median : 6.269 | Median : 6.419 | Median : 4.457 | Median : 4.5396 | Median : 31.378 | Median : 31.377 | Median : 29.22 | Median : 29.22 | Median : 29.22 | Median : 29.22 | Median :0.51936 | Median :0.51936 | Median : 6.876 | Median : 6.952 | Median : 1.091 | Median : 1.1583 | Median : 29.22 | Median : 29.22 | Median : 3.6397 | Median : 3.79987 | Median :0.440428 | Median : 0.46658 | Median : 33.03 | Median : 33.03 | Median : 31.82 | Median : 31.82 | Median : 31.82 | Median : 31.82 | Median :0.6297 | Median :0.6297 | Median : 7.041 | Median : 7.012 | Median : 0.771 | Median : 0.6997 | Median : 31.82 | Median : 31.82 | Median : 3.454 | Median : 3.190 | Median : 0.3643 | Median : 0.3052 | Median : 0.00 | Median : 0.00 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.02957 | Mean : 0.001888 | Mean : 0.0456 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 20.368 | Mean : 20.975 | Mean : 19.939 | Mean : 20.531 | Mean : 9.642 | Mean : 10.379 | Mean :0.7622 | Mean :0.75010 | Mean :10.2294 | Mean : 10.5183 | Mean : 5.3749 | Mean : 5.5120 | Mean : 9.642 | Mean : 10.379 | Mean : 6.878 | Mean : 7.226 | Mean : 4.914 | Mean : 5.0591 | Mean : 42.370 | Mean : 42.370 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean :0.51655 | Mean :0.51655 | Mean : 9.574 | Mean : 9.572 | Mean : 1.706 | Mean : 1.7103 | Mean : 40.53 | Mean : 40.53 | Mean : 4.7421 | Mean : 4.89181 | Mean :0.572331 | Mean : 0.64594 | Mean : 43.67 | Mean : 43.67 | Mean : 41.75 | Mean : 41.75 | Mean : 41.75 | Mean : 41.75 | Mean :0.5340 | Mean :0.5340 | Mean : 9.861 | Mean : 9.858 | Mean : 1.755 | Mean : 1.7589 | Mean : 41.75 | Mean : 41.75 | Mean : 4.882 | Mean : 5.035 | Mean : 0.5890 | Mean : 0.6647 | Mean : 1.30 | Mean : 1.30 | Mean : 1.223 | Mean : 1.223 | Mean : 1.223 | Mean : 1.223 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.2868 | Mean : 0.2865 | Mean : 0.04866 | Mean : 0.04868 | Mean : 1.223 | Mean : 1.223 | Mean : 0.1402 | Mean : 0.1436 | Mean : 0.01667 | Mean : 0.01875 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03319 | Mean : 0.03315 | Mean : 0.0319 | Mean : 0.0321 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 48.99 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.65576 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.3387 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 24.197 | 3rd Qu.: 24.924 | 3rd Qu.: 23.647 | 3rd Qu.: 24.391 | 3rd Qu.:10.875 | 3rd Qu.: 11.813 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.:12.0823 | 3rd Qu.: 12.4421 | 3rd Qu.: 6.2943 | 3rd Qu.: 6.4463 | 3rd Qu.:10.875 | 3rd Qu.: 11.813 | 3rd Qu.: 7.763 | 3rd Qu.: 8.080 | 3rd Qu.: 5.530 | 3rd Qu.: 5.6235 | 3rd Qu.: 52.214 | 3rd Qu.: 52.220 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.:11.805 | 3rd Qu.:11.875 | 3rd Qu.: 2.236 | 3rd Qu.: 2.2089 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 5.6271 | 3rd Qu.: 5.80607 | 3rd Qu.:0.679822 | 3rd Qu.: 0.79086 | 3rd Qu.: 61.15 | 3rd Qu.: 61.15 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.: 13.628 | 3rd Qu.: 13.671 | 3rd Qu.: 2.253 | 3rd Qu.: 2.3512 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 6.974 | 3rd Qu.: 7.134 | 3rd Qu.: 0.8258 | 3rd Qu.: 0.8697 | 3rd Qu.: 27.54 | 3rd Qu.: 27.53 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 6.1138 | 3rd Qu.: 6.1253 | 3rd Qu.: 0.92670 | 3rd Qu.: 0.95745 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 3.0444 | 3rd Qu.: 3.0412 | 3rd Qu.: 0.34942 | 3rd Qu.: 0.34882 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8700 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :271.96 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 14.65678 | Max. : 3.040000 | Max. : 436.0988 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :185.424 | Max. :232.948 | Max. :178.526 | Max. :224.272 | Max. :55.562 | Max. :120.912 | Max. :0.9863 | Max. :0.99149 | Max. :89.4354 | Max. :112.2238 | Max. :44.8901 | Max. :56.1999 | Max. :55.562 | Max. :120.912 | Max. :35.282 | Max. :68.300 | Max. :22.404 | Max. :38.5808 | Max. :293.504 | Max. :293.535 | Max. :271.96 | Max. :271.96 | Max. :271.96 | Max. :271.96 | Max. :0.91018 | Max. :0.91018 | Max. :67.727 | Max. :67.883 | Max. :16.603 | Max. :16.8374 | Max. :271.96 | Max. :271.96 | Max. :47.2073 | Max. :58.63388 | Max. :8.194314 | Max. :12.64128 | Max. :622.14 | Max. :622.12 | Max. :576.56 | Max. :576.56 | Max. :576.56 | Max. :576.56 | Max. :1.1573 | Max. :1.1573 | Max. :143.193 | Max. :143.389 | Max. :34.615 | Max. :34.9092 | Max. :576.56 | Max. :576.56 | Max. :77.626 | Max. :88.241 | Max. :11.9413 | Max. :17.4346 | Max. : 328.68 | Max. : 328.67 | Max. : 304.596 | Max. : 304.596 | Max. : 304.596 | Max. : 304.596 | Max. : 0.49844 | Max. : 0.49844 | Max. : 75.6490 | Max. : 75.7526 | Max. : 18.28725 | Max. : 18.44258 | Max. : 304.596 | Max. : 304.596 | Max. : 45.0466 | Max. : 54.4305 | Max. : 8.66973 | Max. : 12.65802 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :6 | NA’s :8 | NA’s :1528 | NA’s :2219 | NA | NA | NA | NA | NA | NA |
table 4.3.2.2C : 41055 x 110 : Summary of Stakes reversed Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.2D : 19 x 6 : PL of Stakes reversed Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
Median Fractional Models
Due to there has no league risk management profile, here I try to use the median value of stakes on every single league as the baseline.
Table 4.3.2.2E : Summary Table of Various Kelly Models (Stakes Reversed based with Median Stakes Adjusted Models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-23.18841 | Min. :-3.480000 | Min. :-488.0000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 1.218 | Min. : 1.203 | Min. : 1.214 | Min. : 1.199 | Min. : 1.942 | Min. : 1.828 | Min. :0.2353 | Min. :0.07552 | Min. : 0.8587 | Min. : 0.8333 | Min. : 0.6467 | Min. : 0.5831 | Min. : 1.942 | Min. : 1.828 | Min. : 1.313 | Min. : 1.152 | Min. : 0.8873 | Min. : 0.7253 | Min. : 1.523 | Min. : 1.524 | Min. : 1.50 | Min. : 1.50 | Min. : 1.50 | Min. : 1.50 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. :0.0000 | Min. :0.0000 | Min. : 1.50 | Min. : 1.50 | Min. : 0.1488 | Min. : 0.02451 | Min. :0.002091 | Min. :0.000008 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. :0.0000 | Min. : 0.0000 | Min. :-172.704 | Min. :-172.732 | Min. :-160.000 | Min. :-160.000 | Min. :-160.000 | Min. :-160.000 | Min. :-0.81996 | Min. :-0.81996 | Min. :-39.7368 | Min. :-39.8932 | Min. :-9.60526 | Min. :-9.83981 | Min. :-160.000 | Min. :-160.000 | Min. :-27.7730 | Min. :-34.4955 | Min. :-4.82088 | Min. :-7.43712 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 22.00 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.67742 | 1st Qu.:-0.040000 | 1st Qu.: -0.9600 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 10.925 | 1st Qu.: 10.689 | 1st Qu.: 10.710 | 1st Qu.: 10.494 | 1st Qu.: 7.073 | 1st Qu.: 6.832 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 5.6282 | 1st Qu.: 5.5260 | 1st Qu.: 3.0815 | 1st Qu.: 3.0344 | 1st Qu.: 7.073 | 1st Qu.: 6.832 | 1st Qu.: 5.161 | 1st Qu.: 5.044 | 1st Qu.: 3.7588 | 1st Qu.: 3.7259 | 1st Qu.: 22.691 | 1st Qu.: 22.682 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 4.859 | 1st Qu.: 4.869 | 1st Qu.:0.5000 | 1st Qu.:0.4650 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 2.4176 | 1st Qu.: 2.29810 | 1st Qu.:0.262222 | 1st Qu.:0.230042 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.:0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -24.049 | 1st Qu.: -24.051 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -5.2500 | 1st Qu.: -5.2708 | 1st Qu.:-0.66346 | 1st Qu.:-0.69065 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -2.7099 | 1st Qu.: -2.7027 | 1st Qu.:-0.31171 | 1st Qu.:-0.32083 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 13.668 | Median : 14.089 | Median : 13.374 | Median : 13.766 | Median : 8.198 | Median : 8.400 | Median :0.7693 | Median :0.76495 | Median : 6.9444 | Median : 7.1396 | Median : 3.7301 | Median : 3.8140 | Median : 8.198 | Median : 8.400 | Median : 5.850 | Median : 5.966 | Median : 4.1802 | Median : 4.2229 | Median : 27.713 | Median : 27.705 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median :0.51936 | Median :0.51936 | Median : 6.037 | Median : 6.072 | Median :0.8616 | Median :0.9065 | Median : 26.00 | Median : 26.00 | Median : 3.1589 | Median : 3.27612 | Median :0.379728 | Median :0.401914 | Median : 29.87 | Median : 29.88 | Median : 28.88 | Median : 28.88 | Median : 28.88 | Median : 28.88 | Median :0.6297 | Median :0.6297 | Median : 6.287 | Median : 6.260 | Median : 0.5621 | Median : 0.4888 | Median : 28.88 | Median : 28.88 | Median : 3.058 | Median : 2.796 | Median :0.3180 | Median : 0.2651 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 33.26 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.03312 | Mean : 0.001888 | Mean : 0.0517 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 16.808 | Mean : 17.303 | Mean : 16.457 | Mean : 16.941 | Mean : 8.832 | Mean : 9.430 | Mean :0.7622 | Mean :0.75010 | Mean : 8.4889 | Mean : 8.7232 | Mean : 4.5046 | Mean : 4.6144 | Mean : 8.832 | Mean : 9.430 | Mean : 6.303 | Mean : 6.578 | Mean : 4.5051 | Mean : 4.6130 | Mean : 34.763 | Mean : 34.763 | Mean : 33.26 | Mean : 33.26 | Mean : 33.26 | Mean : 33.26 | Mean :0.51655 | Mean :0.51655 | Mean : 7.756 | Mean : 7.754 | Mean :1.2544 | Mean :1.2619 | Mean : 33.26 | Mean : 33.26 | Mean : 3.8925 | Mean : 4.01581 | Mean :0.469751 | Mean :0.529957 | Mean : 35.84 | Mean : 35.84 | Mean : 34.27 | Mean : 34.27 | Mean : 34.27 | Mean : 34.27 | Mean :0.5340 | Mean :0.5340 | Mean : 7.991 | Mean : 7.988 | Mean : 1.2900 | Mean : 1.2976 | Mean : 34.27 | Mean : 34.27 | Mean : 4.009 | Mean : 4.135 | Mean :0.4836 | Mean : 0.5455 | Mean : 1.076 | Mean : 1.076 | Mean : 1.012 | Mean : 1.012 | Mean : 1.012 | Mean : 1.012 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.2342 | Mean : 0.2339 | Mean : 0.03561 | Mean : 0.03568 | Mean : 1.012 | Mean : 1.012 | Mean : 0.1163 | Mean : 0.1192 | Mean : 0.01383 | Mean : 0.01556 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03333 | Mean : 0.03316 | Mean : 0.0316 | Mean : 0.0318 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 36.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.76522 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.1500 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 18.782 | 3rd Qu.: 20.154 | 3rd Qu.: 18.408 | 3rd Qu.: 19.756 | 3rd Qu.: 9.835 | 3rd Qu.:10.735 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.: 9.4405 | 3rd Qu.:10.0885 | 3rd Qu.: 4.9571 | 3rd Qu.: 5.2729 | 3rd Qu.: 9.835 | 3rd Qu.:10.735 | 3rd Qu.: 6.986 | 3rd Qu.: 7.315 | 3rd Qu.: 4.9302 | 3rd Qu.: 5.0676 | 3rd Qu.: 37.799 | 3rd Qu.: 37.792 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.: 8.462 | 3rd Qu.: 8.484 | 3rd Qu.:1.4706 | 3rd Qu.:1.5750 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 4.4753 | 3rd Qu.: 4.74630 | 3rd Qu.:0.556958 | 3rd Qu.:0.664037 | 3rd Qu.: 53.19 | 3rd Qu.: 53.19 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.:11.733 | 3rd Qu.:11.770 | 3rd Qu.: 1.7185 | 3rd Qu.: 1.8028 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 5.954 | 3rd Qu.: 6.062 | 3rd Qu.:0.7047 | 3rd Qu.: 0.7407 | 3rd Qu.: 23.862 | 3rd Qu.: 23.859 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 5.2225 | 3rd Qu.: 5.2377 | 3rd Qu.: 0.70188 | 3rd Qu.: 0.73349 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 2.6275 | 3rd Qu.: 2.6143 | 3rd Qu.: 0.30138 | 3rd Qu.: 0.29988 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8800 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :160.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 22.98286 | Max. : 3.040000 | Max. : 256.0000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :109.231 | Max. :137.120 | Max. :105.172 | Max. :132.016 | Max. :39.250 | Max. :78.096 | Max. :0.9863 | Max. :0.99149 | Max. :52.7586 | Max. :66.0960 | Max. :26.5517 | Max. :33.1360 | Max. :39.250 | Max. :78.096 | Max. :24.923 | Max. :44.115 | Max. :15.8264 | Max. :24.9192 | Max. :172.706 | Max. :172.737 | Max. :160.00 | Max. :160.00 | Max. :160.00 | Max. :160.00 | Max. :0.91018 | Max. :0.91018 | Max. :39.737 | Max. :39.893 | Max. :9.6053 | Max. :9.8398 | Max. :160.00 | Max. :160.00 | Max. :27.7730 | Max. :34.49549 | Max. :4.820880 | Max. :7.437118 | Max. :366.05 | Max. :366.03 | Max. :339.20 | Max. :339.20 | Max. :339.20 | Max. :339.20 | Max. :1.1573 | Max. :1.1573 | Max. :83.854 | Max. :84.050 | Max. :19.7804 | Max. :20.0744 | Max. :339.20 | Max. :339.20 | Max. :50.579 | Max. :61.115 | Max. :9.7345 | Max. :14.2126 | Max. : 193.384 | Max. : 193.375 | Max. : 190.800 | Max. : 190.800 | Max. : 190.800 | Max. : 190.800 | Max. : 0.49844 | Max. : 0.49844 | Max. : 47.2000 | Max. : 47.5617 | Max. :11.17500 | Max. :11.71758 | Max. : 190.800 | Max. : 190.800 | Max. : 36.7216 | Max. : 44.3713 | Max. : 7.06750 | Max. :10.31873 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :19 | NA’s :16 | NA’s :2026 | NA’s :3114 | NA | NA | NA | NA | NA | NA |
table 4.3.2.2E : 41055 x 110 : Summary of Stakes reversed Kelly models (median value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.2F : 19 x 6 : PL of Stakes reversed Kelly models year (median value of stakes as staking adjuster) 2011~2015.
Basic Fractional Models
rEMProbB (real EM Probabilities Back) are the application of the parameter from reversion of the stakes where add-on some modified version Kelly models. For the EM probabilities based models, I had just simply adjusted for staking and get the different outcome of Profit & Loss.
Table 4.3.2.3 : Summary Table of Various Kelly Models (reversed rEMProbB based models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 0.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-1.0000 | Min. :-3.480000 | Min. :-5568.000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 12.50 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.:-1.0000 | 1st Qu.:-0.040000 | 1st Qu.: -0.780 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.0000 | Median : 0.000000 | Median : 0.000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.0332 | Mean : 0.001888 | Mean : -0.123 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 50.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.8500 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.080 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :1600.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 2.6550 | Max. : 3.040000 | Max. : 4864.000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.2.3A : 41055 x 92 : Summary of Reversed rEMProbB Kelly models year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.3B : 19 x 5 : PL of Reversed rEMProbB Kelly models year 2011~2015.
Mean Fractional Models
Due to there has no league risk management profile, here I try to use the mean value of stakes on every single league as the baseline.
Table 4.3.2.3C : Summary Table of Various Kelly Models (Reversed rEMProbB based with Mean Stakes Adjusted models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.80 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-11.15344 | Min. :-3.480000 | Min. :-829.4804 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 24.74 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.57965 | 1st Qu.:-0.040000 | 1st Qu.: -1.0939 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 29.22 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.02957 | Mean : 0.001888 | Mean : 0.0456 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 48.99 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.65576 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.3387 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :271.96 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 14.65678 | Max. : 3.040000 | Max. : 436.0988 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.2.3C : 41055 x 92 : Summary of Reversed rEMProbB Kelly models year (mean value of stakes as staking adjuster) 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.3D : 19 x 5 : PL of Reversed rEMProbB Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
Median Fractional Models
Due to there has no league risk management profile, here I try to use the median value of stakes on every single league as the baseline.
Table 4.3.2.3E : Summary Table of Various Kelly Models (Reversed rEMProbB based with Mean Stakes Adjusted models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-23.18841 | Min. :-3.480000 | Min. :-488.0000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 22.00 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.67742 | 1st Qu.:-0.040000 | 1st Qu.: -0.9600 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 33.26 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.03312 | Mean : 0.001888 | Mean : 0.0517 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 36.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.76522 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.1500 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :160.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 22.98286 | Max. : 3.040000 | Max. : 256.0000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.2.3E : 41055 x 92 : Summary of Reversed rEMProbB Kelly models year (median value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.2.3F : 19 x 5 : PL of Reversed rEMProbB Kelly models (median value of stakes as staking adjuster) year 2011~2015.
vKelly2(dat)$Kelly1$data %>% select(rEMProbB, netProbB, netEMEdge) %>% colMeans
# rEMProbB netProbB netEMEdge
# 0.5165538 0.5056328 1.0216569
#'@ 0.5165538 / 0.5056328
[1] 1.021599
# 2.62% (rank: 18)
# 3.09% (rank: 04)
# 3.09% (rank: 03)
#'@ 2.62 * 1.021599
[1] 2.676589
From above various Kelly models, we can know from the P&L which the Kelly models have filter and risk averse to improve the total profit across the years. There has a remark which is the variables \(\rho_{i}\) in the Kelly models for both PropHKPriceEdge and PropnetProbBEdge is reversed from rEMProbB * netEMEdge and the \(rEMProbB_{i} = \frac{PL_{year_j}}{Stakes_{year_j}} \times netProb_{i}\). Therefore there will be double edge applied to the rEMProb while we can know the additional edge of 1.021599 might increase the profit from 2.62% to 3.09% to the mean value sample data. However a random staking simulation required and later will use runif(n, min = 0, max = 1) and rnorm(n, mean = 0, sd = 1) to test the result.
Base on Bayesian anlaysis, KEMProbnetProbB and follow by KEMProb will be the best model for static model while we will need to test the posterior analysis by application of Monte Carlo method in later section.
In previous section I measure the data from 2011~2015 as static analysis. Well, now I try to seperates as annum data base and get the optimal weight value for next year use. Due to I dont know if the weight function is needed for staking models since sports consultancy firm had applied Poison models weith weight function. I don’t pretand to know and only simulate it by obseravation to guess the optimal value.
Due to fractional Kelly model is independent models (for example : half-Kelly will be half-Kelly staking model, and full-Kelly will be only full-Kelly model across the years as we made comparison in section [4.3.2 Fractional Kelly odel].), now we need to make it dynamic fractional model. Similar with my prevous Rmodel which applied on Poisson model. Due to the calculation of the settlement and result on the win and loss of Asian Handicap is different with Fixed odds, the probabilities of the outcome will be descrete and the measurement of the likelihood result required in order to maximize the profit. here we need to add an additional parameter controller to adjust the staking amount on every single match.
Now I try to will simulate an enhanced Kelly model on staking which take the effect of the outcome of the result into calculation below controller parameter \(\phi(r)\) fit into \(equation\ 4.3.3.1\) to control the leverage ratio.30 similar theory apply on investment portfolio while it might turn to be nested controller parameters across different soccer leagues.
\[\phi(r) = exp(w_{i}\rho_{i}) \cdots equation\ 4.3.3.1\] Where \(X = x_{i,2,3...n}\) is the original staking amount by Kelly model. Meanwhile, the \(r\) value is the optimal parameter controller for staking.
\[r\begin{Bmatrix} =& Win\\ =& Half\ Win\\ =& Push\\ =& Half\ Loss\\ =& Loss\end{Bmatrix} \cdots equation\ 4.3.3.2\]
## I dont pretand to know the true weight function, here I try both methods bewlo to do the comparison.
## option 1
- $\theta$ = 1 if Win
= 0.5 if Win-Half
= 0 if push
= -0.5 if Loss-Half
= -1 if Loss
## option 2
- 5 dummy variables which are :
win = ifelse(1, 0)
win-half = ifelse(1, 0)
push = ifelse(1, 0)
loss-half = ifelse(1, 0)
loss = ifelse(1, 0)
## Need to correct the content, below just a sample...
## Random pick 2 observations among each stratified levels of Result.
K <- llply(split(dat, dat$Result), function(x) x[sample(nrow(x), 2), c('Result', 'Return', 'EUPrice', 'HKPrice', 'Stakes', 'Rebates')]) %>% ldply(., .id = 'Result') %>% mutate(KReturn = currency(Return), Return = currency(Return), KStakes = currency(Stakes), Stakes = currency(Stakes), Rebates = percent(Rebates), Change = percent(KStakes / Stakes - 1)) %>% .[sample(nrow(.), nrow(.)), ]
## http://www.w3schools.com/colors/colors_picker.asp
K %>% formattable(list(
Result = formatter('span', style = x ~ ifelse(x == 'Win', style(color = '#269900', font.weight = 'bold'), ifelse(x == 'Half Win', style(color = '#40FF00'), ifelse(x == 'Push', style(color = '#FFFF00'), ifelse(x == 'Half Loss', style(color = '#FF8C1A'), ifelse(x == 'Loss', style(color = '#FF0000', font.weight = 'bold'), NA)))))),
KReturn = formatter('span', style = ~ style(color = ifelse(KReturn >= KStakes, 'green', 'red')), ~ icontext(ifelse(KReturn >= KStakes, 'plus-sign', 'minus-sign'), KReturn)),
Return = formatter('span', style = ~ style(color = ifelse(Return >= Stakes, 'green', 'red')), ~ icontext(ifelse(Return >= Stakes, 'plus-sign', 'minus-sign'), Return)),
EUPrice = color_tile('white', '#003D99'),
HKPrice = color_tile('white', '#003D99'),
KStakes = color_tile('white', '#CC9900'),
Stakes = color_tile('white', '#CC9900'),
Change = formatter('span', style = ~ style(color = ifelse(Change < 0, 'red', 'green')), ~ icontext(ifelse(Change < 0, 'arrow-down', 'arrow-up'), Change))))
| Result | Return | EUPrice | HKPrice | Stakes | Rebates | KReturn | KStakes | Change | |
|---|---|---|---|---|---|---|---|---|---|
| 8 | Loss | $0.00 | 1.65 | 0.65 | $7.00 | -1.00% | $0.00 | $7.00 | 0.00% |
| 6 | Half Win | $4.71 | 2.14 | 1.14 | $3.00 | 0.00% | $4.71 | $3.00 | 0.00% |
| 10 | Push | $44.00 | 1.98 | 0.98 | $44.00 | 0.00% | $44.00 | $44.00 | 0.00% |
| 1 | Cancelled | $1.00 | 2.37 | 1.37 | $1.00 | 0.00% | $1.00 | $1.00 | 0.00% |
| 3 | Half Loss | $1.00 | 1.68 | 0.68 | $2.00 | 0.00% | $1.00 | $2.00 | 0.00% |
| 11 | Win | $355.30 | 1.87 | 0.87 | $190.00 | 35.00% | $355.30 | $190.00 | 0.00% |
| 12 | Win | $107.46 | 1.99 | 0.99 | $54.00 | 12.00% | $107.46 | $54.00 | 0.00% |
| 9 | Push | $10.00 | 1.61 | 0.61 | $10.00 | 0.00% | $10.00 | $10.00 | 0.00% |
| 7 | Loss | $0.00 | 1.62 | 0.62 | $19.00 | -4.00% | $0.00 | $19.00 | 0.00% |
| 2 | Cancelled | $13.00 | 2.09 | 1.09 | $13.00 | 0.00% | $13.00 | $13.00 | 0.00% |
| 5 | Half Win | $27.29 | 2.21 | 1.21 | $17.00 | 2.00% | $27.29 | $17.00 | 0.00% |
| 4 | Half Loss | $125.50 | 2.01 | 1.01 | $251.00 | -26.00% | $125.50 | $251.00 | 0.00% |
table 4.3.3.1 : 12 x 9 : Kelly stakes and firm A’s stakes of annually investment summary table.31 The annum return rates but not all data return rates since we need to use the return of that particular year to reverse. The weight parameter in later section will take last year performance to be weight controller. Due to the firm A does not only placed bets with one agent but couples of agencies. Let say placed one millions HKD on a soccer match with higher price simultaniously compare to placed bets on one agency with price decreasingly, therefore the Kelly stakes will definately defferent with firm A’s stakes.
- in order to save the executive time, here I load the saved RData file which has simulate to get the optimal weight value. Now I try to fit the weight parameter into the Kelly model to get the result and doing comparison as below.
Weighted Fractional Models
Stakes based reversed Kelly models are the application of the parameter from reversion of the stakes where add-on some modified version Kelly models. I tried to adjust the stakes to get the outcome of PL result.
Table 4.3.2.2A : Summary Table of Various Kelly Models (Stakes reversed based models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 0.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-1.0000 | Min. :-3.480000 | Min. :-5568.000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 0.7164 | Min. : 0.6632 | Min. : 0.7101 | Min. : 0.656 | Min. : 1.018 | Min. : 0.8478 | Min. :0.2353 | Min. :0.07552 | Min. : 0.5651 | Min. : 0.4839 | Min. : 0.4062 | Min. : 0.2808 | Min. : 1.018 | Min. : 0.8478 | Min. : 0.6814 | Min. : 0.5262 | Min. : 0.411 | Min. : 0.2758 | Min. : 0.5113 | Min. : 0.5095 | Min. : 0.50 | Min. : 0.50 | Min. : 0.50 | Min. : 0.50 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. : 0.50 | Min. : 0.50 | Min. : 0.04419 | Min. : 0.0186 | Min. : 0.001752 | Min. : 0.00001 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. :-1703.881 | Min. :-1703.877 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-0.81996 | Min. :-0.81996 | Min. :-399.5146 | Min. :-399.5869 | Min. :-99.2718 | Min. :-99.38039 | Min. :-1600.0000 | Min. :-1600.0000 | Min. :-204.07878 | Min. :-225.6129 | Min. :-26.03009 | Min. :-31.81324 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00 | Min. :-1.00 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 12.50 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.:-1.0000 | 1st Qu.:-0.040000 | 1st Qu.: -0.780 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 6.5857 | 1st Qu.: 6.6500 | 1st Qu.: 6.4545 | 1st Qu.: 6.513 | 1st Qu.: 5.562 | 1st Qu.: 5.5095 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 3.4912 | 1st Qu.: 3.5105 | 1st Qu.: 2.0090 | 1st Qu.: 2.0105 | 1st Qu.: 5.562 | 1st Qu.: 5.5095 | 1st Qu.: 4.0210 | 1st Qu.: 4.0020 | 1st Qu.: 2.900 | 1st Qu.: 2.8978 | 1st Qu.: 13.1445 | 1st Qu.: 13.1429 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 2.574 | 1st Qu.: 2.575 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: 12.50 | 1st Qu.: 12.50 | 1st Qu.: 1.42401 | 1st Qu.: 1.3993 | 1st Qu.: 0.162111 | 1st Qu.: 0.15220 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -18.394 | 1st Qu.: -18.402 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -3.9845 | 1st Qu.: -3.9845 | 1st Qu.: -0.4068 | 1st Qu.: -0.44459 | 1st Qu.: -18.0000 | 1st Qu.: -18.0000 | 1st Qu.: -2.09361 | 1st Qu.: -2.1492 | 1st Qu.: -0.24835 | 1st Qu.: -0.26395 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00 | 1st Qu.:-1.00 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.0000 | Median : 0.000000 | Median : 0.000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 13.3921 | Median : 13.5570 | Median : 13.1134 | Median : 13.274 | Median : 8.005 | Median : 8.1081 | Median :0.7693 | Median :0.76495 | Median : 6.8155 | Median : 6.8944 | Median : 3.6711 | Median : 3.6931 | Median : 8.005 | Median : 8.1081 | Median : 5.7454 | Median : 5.7943 | Median : 4.139 | Median : 4.1400 | Median : 27.3565 | Median : 27.3569 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median :0.51936 | Median :0.51936 | Median : 6.045 | Median : 6.048 | Median : 0.8272 | Median : 0.8439 | Median : 26.00 | Median : 26.00 | Median : 3.05504 | Median : 3.0992 | Median : 0.359275 | Median : 0.37422 | Median : 16.87 | Median : 16.87 | Median : 16.00 | Median : 16.00 | Median : 16.00 | Median : 16.00 | Median :0.6297 | Median :0.6297 | Median : 3.242 | Median : 3.216 | Median : 0.000 | Median : 0.000 | Median : 16.00 | Median : 16.00 | Median : 1.788 | Median : 1.708 | Median : 0.1975 | Median : 0.1781 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00 | Median : 0.00 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.0332 | Mean : 0.001888 | Mean : -0.123 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 20.2975 | Mean : 20.7183 | Mean : 19.8809 | Mean : 20.292 | Mean : 8.766 | Mean : 9.1770 | Mean :0.7622 | Mean :0.75010 | Mean : 10.2006 | Mean : 10.3990 | Mean : 5.3605 | Mean : 5.4523 | Mean : 8.766 | Mean : 9.1770 | Mean : 6.2743 | Mean : 6.4657 | Mean : 4.496 | Mean : 4.5732 | Mean : 42.3180 | Mean : 42.3180 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean :0.51655 | Mean :0.51655 | Mean : 9.582 | Mean : 9.583 | Mean : 1.8106 | Mean : 1.8265 | Mean : 40.53 | Mean : 40.53 | Mean : 4.73391 | Mean : 4.8490 | Mean : 0.562677 | Mean : 0.61187 | Mean : 43.24 | Mean : 43.24 | Mean : 41.40 | Mean : 41.40 | Mean : 41.40 | Mean : 41.40 | Mean :0.5340 | Mean :0.5340 | Mean : 9.781 | Mean : 9.783 | Mean : 1.842 | Mean : 1.858 | Mean : 41.40 | Mean : 41.40 | Mean : 4.833 | Mean : 4.949 | Mean : 0.5742 | Mean : 0.6242 | Mean : 0.926 | Mean : 0.926 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.1994 | Mean : 0.1992 | Mean : 0.0310 | Mean : 0.03177 | Mean : 0.8717 | Mean : 0.8717 | Mean : 0.09928 | Mean : 0.1003 | Mean : 0.01157 | Mean : 0.01232 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.0328 | Mean : 0.0329 | Mean : 0.03 | Mean : 0.03 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 50.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.8500 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.080 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 24.3364 | 3rd Qu.: 24.8399 | 3rd Qu.: 23.8376 | 3rd Qu.: 24.332 | 3rd Qu.:10.885 | 3rd Qu.: 11.3964 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.: 12.1869 | 3rd Qu.: 12.4157 | 3rd Qu.: 6.3529 | 3rd Qu.: 6.4489 | 3rd Qu.:10.885 | 3rd Qu.: 11.3964 | 3rd Qu.: 7.7735 | 3rd Qu.: 7.9939 | 3rd Qu.: 5.561 | 3rd Qu.: 5.6439 | 3rd Qu.: 51.1809 | 3rd Qu.: 51.1847 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.: 11.806 | 3rd Qu.: 11.782 | 3rd Qu.: 2.2386 | 3rd Qu.: 2.2458 | 3rd Qu.: 50.00 | 3rd Qu.: 50.00 | 3rd Qu.: 5.69606 | 3rd Qu.: 5.8483 | 3rd Qu.: 0.681064 | 3rd Qu.: 0.74440 | 3rd Qu.: 55.84 | 3rd Qu.: 55.84 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.: 12.458 | 3rd Qu.: 12.439 | 3rd Qu.: 1.980 | 3rd Qu.: 2.021 | 3rd Qu.: 53.55 | 3rd Qu.: 53.55 | 3rd Qu.: 6.160 | 3rd Qu.: 6.223 | 3rd Qu.: 0.7218 | 3rd Qu.: 0.7632 | 3rd Qu.: 21.232 | 3rd Qu.: 21.230 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 4.6300 | 3rd Qu.: 4.6499 | 3rd Qu.: 0.5975 | 3rd Qu.: 0.62808 | 3rd Qu.: 20.2800 | 3rd Qu.: 20.2800 | 3rd Qu.: 2.36233 | 3rd Qu.: 2.3670 | 3rd Qu.: 0.27408 | 3rd Qu.: 0.28592 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.88 | 3rd Qu.: 0.90 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :1600.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 2.6550 | Max. : 3.040000 | Max. : 4864.000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :838.2473 | Max. :904.5996 | Max. :812.3153 | Max. :876.612 | Max. :69.868 | Max. :111.6521 | Max. :0.9863 | Max. :0.99149 | Max. :406.4039 | Max. :438.5324 | Max. :203.4483 | Max. :219.4924 | Max. :69.868 | Max. :111.6521 | Max. :48.6334 | Max. :72.2019 | Max. :34.213 | Max. :46.6908 | Max. :1703.8836 | Max. :1703.8839 | Max. :1600.00 | Max. :1600.00 | Max. :1600.00 | Max. :1600.00 | Max. :0.91018 | Max. :0.91018 | Max. :399.515 | Max. :399.587 | Max. :99.2718 | Max. :99.3804 | Max. :1600.00 | Max. :1600.00 | Max. :204.07878 | Max. :225.6129 | Max. :26.030094 | Max. :31.81324 | Max. :3186.26 | Max. :3186.26 | Max. :2992.00 | Max. :2992.00 | Max. :2992.00 | Max. :2992.00 | Max. :1.1573 | Max. :1.1573 | Max. :746.925 | Max. :746.915 | Max. :185.388 | Max. :185.372 | Max. :2992.00 | Max. :2992.00 | Max. :337.202 | Max. :334.563 | Max. :38.0031 | Max. :40.2482 | Max. : 1482.379 | Max. : 1482.379 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 0.49844 | Max. : 0.49844 | Max. : 347.5000 | Max. : 347.4951 | Max. : 86.2500 | Max. : 86.24260 | Max. : 1392.0000 | Max. : 1392.0000 | Max. : 156.88006 | Max. : 155.6523 | Max. : 17.68057 | Max. : 17.40491 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65 | Max. : 2.65 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :1348 | NA’s :1383 | NA’s :10832 | NA’s :10297 | NA | NA | NA | NA | NA | NA |
table 4.3.3.2A : 41055 x 110 : Summary of Stakes reversed weighted Kelly models year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.2B : 19 x 6 : PL of Stakes based reversed weighted Kelly models year 2011~2015.
Mean Fractional Models
Due to there has no league risk management profile, here I try to use the mean value of stakes on every single league as the baseline.
Table 4.3.2.2C : Summary Table of Various Kelly Models (Stakes Reversed based with Mean Stakes Adjusted Models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.80 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-11.15344 | Min. :-3.480000 | Min. :-829.4804 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 1.355 | Min. : 1.336 | Min. : 1.351 | Min. : 1.332 | Min. : 2.186 | Min. : 2.130 | Min. :0.2353 | Min. :0.07552 | Min. : 0.9472 | Min. : 0.9408 | Min. : 0.7094 | Min. : 0.6746 | Min. : 2.186 | Min. : 2.130 | Min. : 1.516 | Min. : 1.413 | Min. : 1.051 | Min. : 0.9378 | Min. : 1.826 | Min. : 1.827 | Min. : 1.80 | Min. : 1.80 | Min. : 1.80 | Min. : 1.80 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 1.80 | Min. : 1.80 | Min. : 0.1804 | Min. : 0.02953 | Min. :0.002519 | Min. : 0.00001 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. :-293.50 | Min. :-293.53 | Min. :-271.961 | Min. :-271.961 | Min. :-271.961 | Min. :-271.961 | Min. :-0.81996 | Min. :-0.81996 | Min. :-67.7270 | Min. :-67.8834 | Min. :-16.60281 | Min. :-16.83735 | Min. :-271.961 | Min. :-271.961 | Min. :-47.2073 | Min. :-58.6339 | Min. :-8.19431 | Min. :-12.64128 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 24.74 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.57965 | 1st Qu.:-0.040000 | 1st Qu.: -1.0939 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 12.283 | 1st Qu.: 11.969 | 1st Qu.: 12.053 | 1st Qu.: 11.736 | 1st Qu.: 7.465 | 1st Qu.: 7.210 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 6.3027 | 1st Qu.: 6.1502 | 1st Qu.: 3.4194 | 1st Qu.: 3.3464 | 1st Qu.: 7.465 | 1st Qu.: 7.210 | 1st Qu.: 5.445 | 1st Qu.: 5.322 | 1st Qu.: 3.985 | 1st Qu.: 3.9264 | 1st Qu.: 25.875 | 1st Qu.: 25.877 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 5.629 | 1st Qu.: 5.631 | 1st Qu.: 0.683 | 1st Qu.: 0.6385 | 1st Qu.: 24.74 | 1st Qu.: 24.74 | 1st Qu.: 2.7283 | 1st Qu.: 2.59540 | 1st Qu.:0.296708 | 1st Qu.: 0.26185 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -27.71 | 1st Qu.: -27.71 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -6.0601 | 1st Qu.: -6.1016 | 1st Qu.: -0.87215 | 1st Qu.: -0.90198 | 1st Qu.: -25.881 | 1st Qu.: -25.881 | 1st Qu.: -3.1072 | 1st Qu.: -3.1151 | 1st Qu.:-0.35981 | 1st Qu.: -0.37010 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 29.22 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 15.523 | Median : 16.232 | Median : 15.202 | Median : 15.884 | Median : 8.805 | Median : 9.026 | Median :0.7693 | Median :0.76495 | Median : 7.8573 | Median : 8.1836 | Median : 4.1777 | Median : 4.3292 | Median : 8.805 | Median : 9.026 | Median : 6.269 | Median : 6.419 | Median : 4.457 | Median : 4.5396 | Median : 31.378 | Median : 31.377 | Median : 29.22 | Median : 29.22 | Median : 29.22 | Median : 29.22 | Median :0.51936 | Median :0.51936 | Median : 6.876 | Median : 6.952 | Median : 1.091 | Median : 1.1583 | Median : 29.22 | Median : 29.22 | Median : 3.6397 | Median : 3.79987 | Median :0.440428 | Median : 0.46658 | Median : 33.03 | Median : 33.03 | Median : 31.82 | Median : 31.82 | Median : 31.82 | Median : 31.82 | Median :0.6297 | Median :0.6297 | Median : 7.041 | Median : 7.012 | Median : 0.771 | Median : 0.6997 | Median : 31.82 | Median : 31.82 | Median : 3.454 | Median : 3.190 | Median : 0.3643 | Median : 0.3052 | Median : 0.00 | Median : 0.00 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.02957 | Mean : 0.001888 | Mean : 0.0456 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 20.368 | Mean : 20.975 | Mean : 19.939 | Mean : 20.531 | Mean : 9.642 | Mean : 10.379 | Mean :0.7622 | Mean :0.75010 | Mean :10.2294 | Mean : 10.5183 | Mean : 5.3749 | Mean : 5.5120 | Mean : 9.642 | Mean : 10.379 | Mean : 6.878 | Mean : 7.226 | Mean : 4.914 | Mean : 5.0591 | Mean : 42.370 | Mean : 42.370 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean : 40.53 | Mean :0.51655 | Mean :0.51655 | Mean : 9.574 | Mean : 9.572 | Mean : 1.706 | Mean : 1.7103 | Mean : 40.53 | Mean : 40.53 | Mean : 4.7421 | Mean : 4.89181 | Mean :0.572331 | Mean : 0.64594 | Mean : 43.67 | Mean : 43.67 | Mean : 41.75 | Mean : 41.75 | Mean : 41.75 | Mean : 41.75 | Mean :0.5340 | Mean :0.5340 | Mean : 9.861 | Mean : 9.858 | Mean : 1.755 | Mean : 1.7589 | Mean : 41.75 | Mean : 41.75 | Mean : 4.882 | Mean : 5.035 | Mean : 0.5890 | Mean : 0.6647 | Mean : 1.30 | Mean : 1.30 | Mean : 1.223 | Mean : 1.223 | Mean : 1.223 | Mean : 1.223 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.2868 | Mean : 0.2865 | Mean : 0.04866 | Mean : 0.04868 | Mean : 1.223 | Mean : 1.223 | Mean : 0.1402 | Mean : 0.1436 | Mean : 0.01667 | Mean : 0.01875 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03319 | Mean : 0.03315 | Mean : 0.0319 | Mean : 0.0321 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 48.99 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.65576 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.3387 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 24.197 | 3rd Qu.: 24.924 | 3rd Qu.: 23.647 | 3rd Qu.: 24.391 | 3rd Qu.:10.875 | 3rd Qu.: 11.813 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.:12.0823 | 3rd Qu.: 12.4421 | 3rd Qu.: 6.2943 | 3rd Qu.: 6.4463 | 3rd Qu.:10.875 | 3rd Qu.: 11.813 | 3rd Qu.: 7.763 | 3rd Qu.: 8.080 | 3rd Qu.: 5.530 | 3rd Qu.: 5.6235 | 3rd Qu.: 52.214 | 3rd Qu.: 52.220 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.:11.805 | 3rd Qu.:11.875 | 3rd Qu.: 2.236 | 3rd Qu.: 2.2089 | 3rd Qu.: 48.99 | 3rd Qu.: 48.99 | 3rd Qu.: 5.6271 | 3rd Qu.: 5.80607 | 3rd Qu.:0.679822 | 3rd Qu.: 0.79086 | 3rd Qu.: 61.15 | 3rd Qu.: 61.15 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.: 13.628 | 3rd Qu.: 13.671 | 3rd Qu.: 2.253 | 3rd Qu.: 2.3512 | 3rd Qu.: 58.21 | 3rd Qu.: 58.21 | 3rd Qu.: 6.974 | 3rd Qu.: 7.134 | 3rd Qu.: 0.8258 | 3rd Qu.: 0.8697 | 3rd Qu.: 27.54 | 3rd Qu.: 27.53 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 6.1138 | 3rd Qu.: 6.1253 | 3rd Qu.: 0.92670 | 3rd Qu.: 0.95745 | 3rd Qu.: 26.338 | 3rd Qu.: 26.338 | 3rd Qu.: 3.0444 | 3rd Qu.: 3.0412 | 3rd Qu.: 0.34942 | 3rd Qu.: 0.34882 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8700 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :271.96 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 14.65678 | Max. : 3.040000 | Max. : 436.0988 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :185.424 | Max. :232.948 | Max. :178.526 | Max. :224.272 | Max. :55.562 | Max. :120.912 | Max. :0.9863 | Max. :0.99149 | Max. :89.4354 | Max. :112.2238 | Max. :44.8901 | Max. :56.1999 | Max. :55.562 | Max. :120.912 | Max. :35.282 | Max. :68.300 | Max. :22.404 | Max. :38.5808 | Max. :293.504 | Max. :293.535 | Max. :271.96 | Max. :271.96 | Max. :271.96 | Max. :271.96 | Max. :0.91018 | Max. :0.91018 | Max. :67.727 | Max. :67.883 | Max. :16.603 | Max. :16.8374 | Max. :271.96 | Max. :271.96 | Max. :47.2073 | Max. :58.63388 | Max. :8.194314 | Max. :12.64128 | Max. :622.14 | Max. :622.12 | Max. :576.56 | Max. :576.56 | Max. :576.56 | Max. :576.56 | Max. :1.1573 | Max. :1.1573 | Max. :143.193 | Max. :143.389 | Max. :34.615 | Max. :34.9092 | Max. :576.56 | Max. :576.56 | Max. :77.626 | Max. :88.241 | Max. :11.9413 | Max. :17.4346 | Max. : 328.68 | Max. : 328.67 | Max. : 304.596 | Max. : 304.596 | Max. : 304.596 | Max. : 304.596 | Max. : 0.49844 | Max. : 0.49844 | Max. : 75.6490 | Max. : 75.7526 | Max. : 18.28725 | Max. : 18.44258 | Max. : 304.596 | Max. : 304.596 | Max. : 45.0466 | Max. : 54.4305 | Max. : 8.66973 | Max. : 12.65802 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :6 | NA’s :8 | NA’s :1528 | NA’s :2219 | NA | NA | NA | NA | NA | NA |
table 4.3.3.2C : 41055 x 110 : Summary of Stakes reversed weighted Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.2D : 19 x 6 : PL of Stakes reversed weighted Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
Median Fractional Models
Due to there has no league risk management profile, here I try to use the median value of stakes on every single league as the baseline.
Table 4.3.2.2E : Summary Table of Various Kelly Models (Stakes Reversed based with Median Stakes Adjusted Models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | PropHKPriceEdge | PropnetProbBEdge | KProbHKPrice | KProbnetProbB | KProbFixed | KProbFixednetProbB | KEMProb | KEMProbnetProbB | KProbHalf | KProbHalfnetProbB | KProbQuarter | KProbQuarternetProbB | KProbAdj | KProbAdjnetProbB | KHalfAdj | KHalfAdjnetProbB | KEMQuarterAdj | KEMQuarterAdjnetProbB | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-23.18841 | Min. :-3.480000 | Min. :-488.0000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. : 1.218 | Min. : 1.203 | Min. : 1.214 | Min. : 1.199 | Min. : 1.942 | Min. : 1.828 | Min. :0.2353 | Min. :0.07552 | Min. : 0.8587 | Min. : 0.8333 | Min. : 0.6467 | Min. : 0.5831 | Min. : 1.942 | Min. : 1.828 | Min. : 1.313 | Min. : 1.152 | Min. : 0.8873 | Min. : 0.7253 | Min. : 1.523 | Min. : 1.524 | Min. : 1.50 | Min. : 1.50 | Min. : 1.50 | Min. : 1.50 | Min. :0.03861 | Min. :0.03861 | Min. : 0.000 | Min. : 0.000 | Min. :0.0000 | Min. :0.0000 | Min. : 1.50 | Min. : 1.50 | Min. : 0.1488 | Min. : 0.02451 | Min. :0.002091 | Min. :0.000008 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. : 0.00 | Min. :0.0000 | Min. :0.0000 | Min. : 0.000 | Min. : 0.000 | Min. : 0.0000 | Min. : 0.0000 | Min. : 0.00 | Min. : 0.00 | Min. : 0.000 | Min. : 0.000 | Min. :0.0000 | Min. : 0.0000 | Min. :-172.704 | Min. :-172.732 | Min. :-160.000 | Min. :-160.000 | Min. :-160.000 | Min. :-160.000 | Min. :-0.81996 | Min. :-0.81996 | Min. :-39.7368 | Min. :-39.8932 | Min. :-9.60526 | Min. :-9.83981 | Min. :-160.000 | Min. :-160.000 | Min. :-27.7730 | Min. :-34.4955 | Min. :-4.82088 | Min. :-7.43712 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.0000 | Min. :-1.0000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 22.00 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.67742 | 1st Qu.:-0.040000 | 1st Qu.: -0.9600 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.: 10.925 | 1st Qu.: 10.689 | 1st Qu.: 10.710 | 1st Qu.: 10.494 | 1st Qu.: 7.073 | 1st Qu.: 6.832 | 1st Qu.:0.7080 | 1st Qu.:0.68055 | 1st Qu.: 5.6282 | 1st Qu.: 5.5260 | 1st Qu.: 3.0815 | 1st Qu.: 3.0344 | 1st Qu.: 7.073 | 1st Qu.: 6.832 | 1st Qu.: 5.161 | 1st Qu.: 5.044 | 1st Qu.: 3.7588 | 1st Qu.: 3.7259 | 1st Qu.: 22.691 | 1st Qu.: 22.682 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.:0.44021 | 1st Qu.:0.44021 | 1st Qu.: 4.859 | 1st Qu.: 4.869 | 1st Qu.:0.5000 | 1st Qu.:0.4650 | 1st Qu.: 22.00 | 1st Qu.: 22.00 | 1st Qu.: 2.4176 | 1st Qu.: 2.29810 | 1st Qu.:0.262222 | 1st Qu.:0.230042 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.:0.0000 | 1st Qu.:0.0000 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.: 0.0000 | 1st Qu.: 0.0000 | 1st Qu.: 0.00 | 1st Qu.: 0.00 | 1st Qu.: 0.000 | 1st Qu.: 0.000 | 1st Qu.:0.0000 | 1st Qu.: 0.0000 | 1st Qu.: -24.049 | 1st Qu.: -24.051 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.:-0.43679 | 1st Qu.:-0.43679 | 1st Qu.: -5.2500 | 1st Qu.: -5.2708 | 1st Qu.:-0.66346 | 1st Qu.:-0.69065 | 1st Qu.: -23.000 | 1st Qu.: -23.000 | 1st Qu.: -2.7099 | 1st Qu.: -2.7027 | 1st Qu.:-0.31171 | 1st Qu.:-0.32083 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.0000 | 1st Qu.:-1.0000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median : 13.668 | Median : 14.089 | Median : 13.374 | Median : 13.766 | Median : 8.198 | Median : 8.400 | Median :0.7693 | Median :0.76495 | Median : 6.9444 | Median : 7.1396 | Median : 3.7301 | Median : 3.8140 | Median : 8.198 | Median : 8.400 | Median : 5.850 | Median : 5.966 | Median : 4.1802 | Median : 4.2229 | Median : 27.713 | Median : 27.705 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median : 26.00 | Median :0.51936 | Median :0.51936 | Median : 6.037 | Median : 6.072 | Median :0.8616 | Median :0.9065 | Median : 26.00 | Median : 26.00 | Median : 3.1589 | Median : 3.27612 | Median :0.379728 | Median :0.401914 | Median : 29.87 | Median : 29.88 | Median : 28.88 | Median : 28.88 | Median : 28.88 | Median : 28.88 | Median :0.6297 | Median :0.6297 | Median : 6.287 | Median : 6.260 | Median : 0.5621 | Median : 0.4888 | Median : 28.88 | Median : 28.88 | Median : 3.058 | Median : 2.796 | Median :0.3180 | Median : 0.2651 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.000 | Median : 0.000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.0000 | Median : 0.0000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 33.26 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.03312 | Mean : 0.001888 | Mean : 0.0517 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean : 16.808 | Mean : 17.303 | Mean : 16.457 | Mean : 16.941 | Mean : 8.832 | Mean : 9.430 | Mean :0.7622 | Mean :0.75010 | Mean : 8.4889 | Mean : 8.7232 | Mean : 4.5046 | Mean : 4.6144 | Mean : 8.832 | Mean : 9.430 | Mean : 6.303 | Mean : 6.578 | Mean : 4.5051 | Mean : 4.6130 | Mean : 34.763 | Mean : 34.763 | Mean : 33.26 | Mean : 33.26 | Mean : 33.26 | Mean : 33.26 | Mean :0.51655 | Mean :0.51655 | Mean : 7.756 | Mean : 7.754 | Mean :1.2544 | Mean :1.2619 | Mean : 33.26 | Mean : 33.26 | Mean : 3.8925 | Mean : 4.01581 | Mean :0.469751 | Mean :0.529957 | Mean : 35.84 | Mean : 35.84 | Mean : 34.27 | Mean : 34.27 | Mean : 34.27 | Mean : 34.27 | Mean :0.5340 | Mean :0.5340 | Mean : 7.991 | Mean : 7.988 | Mean : 1.2900 | Mean : 1.2976 | Mean : 34.27 | Mean : 34.27 | Mean : 4.009 | Mean : 4.135 | Mean :0.4836 | Mean : 0.5455 | Mean : 1.076 | Mean : 1.076 | Mean : 1.012 | Mean : 1.012 | Mean : 1.012 | Mean : 1.012 | Mean : 0.01749 | Mean : 0.01749 | Mean : 0.2342 | Mean : 0.2339 | Mean : 0.03561 | Mean : 0.03568 | Mean : 1.012 | Mean : 1.012 | Mean : 0.1163 | Mean : 0.1192 | Mean : 0.01383 | Mean : 0.01556 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03333 | Mean : 0.03316 | Mean : 0.0316 | Mean : 0.0318 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 36.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.76522 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.1500 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.: 18.782 | 3rd Qu.: 20.154 | 3rd Qu.: 18.408 | 3rd Qu.: 19.756 | 3rd Qu.: 9.835 | 3rd Qu.:10.735 | 3rd Qu.:0.8232 | 3rd Qu.:0.83305 | 3rd Qu.: 9.4405 | 3rd Qu.:10.0885 | 3rd Qu.: 4.9571 | 3rd Qu.: 5.2729 | 3rd Qu.: 9.835 | 3rd Qu.:10.735 | 3rd Qu.: 6.986 | 3rd Qu.: 7.315 | 3rd Qu.: 4.9302 | 3rd Qu.: 5.0676 | 3rd Qu.: 37.799 | 3rd Qu.: 37.792 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.:0.59796 | 3rd Qu.:0.59796 | 3rd Qu.: 8.462 | 3rd Qu.: 8.484 | 3rd Qu.:1.4706 | 3rd Qu.:1.5750 | 3rd Qu.: 36.00 | 3rd Qu.: 36.00 | 3rd Qu.: 4.4753 | 3rd Qu.: 4.74630 | 3rd Qu.:0.556958 | 3rd Qu.:0.664037 | 3rd Qu.: 53.19 | 3rd Qu.: 53.19 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.:0.9839 | 3rd Qu.:0.9839 | 3rd Qu.:11.733 | 3rd Qu.:11.770 | 3rd Qu.: 1.7185 | 3rd Qu.: 1.8028 | 3rd Qu.: 51.00 | 3rd Qu.: 51.00 | 3rd Qu.: 5.954 | 3rd Qu.: 6.062 | 3rd Qu.:0.7047 | 3rd Qu.: 0.7407 | 3rd Qu.: 23.862 | 3rd Qu.: 23.859 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 0.46620 | 3rd Qu.: 0.46620 | 3rd Qu.: 5.2225 | 3rd Qu.: 5.2377 | 3rd Qu.: 0.70188 | 3rd Qu.: 0.73349 | 3rd Qu.: 22.880 | 3rd Qu.: 22.880 | 3rd Qu.: 2.6275 | 3rd Qu.: 2.6143 | 3rd Qu.: 0.30138 | 3rd Qu.: 0.29988 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.8600 | 3rd Qu.: 0.8800 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :160.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 22.98286 | Max. : 3.040000 | Max. : 256.0000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :109.231 | Max. :137.120 | Max. :105.172 | Max. :132.016 | Max. :39.250 | Max. :78.096 | Max. :0.9863 | Max. :0.99149 | Max. :52.7586 | Max. :66.0960 | Max. :26.5517 | Max. :33.1360 | Max. :39.250 | Max. :78.096 | Max. :24.923 | Max. :44.115 | Max. :15.8264 | Max. :24.9192 | Max. :172.706 | Max. :172.737 | Max. :160.00 | Max. :160.00 | Max. :160.00 | Max. :160.00 | Max. :0.91018 | Max. :0.91018 | Max. :39.737 | Max. :39.893 | Max. :9.6053 | Max. :9.8398 | Max. :160.00 | Max. :160.00 | Max. :27.7730 | Max. :34.49549 | Max. :4.820880 | Max. :7.437118 | Max. :366.05 | Max. :366.03 | Max. :339.20 | Max. :339.20 | Max. :339.20 | Max. :339.20 | Max. :1.1573 | Max. :1.1573 | Max. :83.854 | Max. :84.050 | Max. :19.7804 | Max. :20.0744 | Max. :339.20 | Max. :339.20 | Max. :50.579 | Max. :61.115 | Max. :9.7345 | Max. :14.2126 | Max. : 193.384 | Max. : 193.375 | Max. : 190.800 | Max. : 190.800 | Max. : 190.800 | Max. : 190.800 | Max. : 0.49844 | Max. : 0.49844 | Max. : 47.2000 | Max. : 47.5617 | Max. :11.17500 | Max. :11.71758 | Max. : 190.800 | Max. : 190.800 | Max. : 36.7216 | Max. : 44.3713 | Max. : 7.06750 | Max. :10.31873 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.6500 | Max. : 2.6500 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :19 | NA’s :16 | NA’s :2026 | NA’s :3114 | NA | NA | NA | NA | NA | NA |
table 4.3.3.2E : 41055 x 110 : Summary of Stakes reversed weighted Kelly models (median value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.2F : 19 x 6 : PL of Stakes reversed weighted Kelly models year (median value of stakes as staking adjuster) 2011~2015.
Weighted Fractional Models
rEMProbB (real EM Probabilities Back) are the application of the parameter from reversion of the stakes where add-on some modified version Kelly models. For the EM probabilities based models, I had just simply adjusted for staking and get the different outcome of Profit & Loss.
Table 4.3.2.3 : Summary Table of Various Kelly Models (reversed rEMProbB based models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 0.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-1.0000 | Min. :-3.480000 | Min. :-5568.000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 12.50 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.:-1.0000 | 1st Qu.:-0.040000 | 1st Qu.: -0.780 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.0000 | Median : 0.000000 | Median : 0.000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.0332 | Mean : 0.001888 | Mean : -0.123 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 50.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.8500 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.080 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :1600.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 2.6550 | Max. : 3.040000 | Max. : 4864.000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.3.3A : 41055 x 92 : Summary of Reversed rEMProbB weighted Kelly models year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.3B : 19 x 5 : PL of Reversed rEMProbB weighted Kelly models year 2011~2015.
Mean Fractional Models
Due to there has no league risk management profile, here I try to use the mean value of stakes on every single league as the baseline.
Table 4.3.2.3C : Summary Table of Various Kelly Models (Reversed rEMProbB based with Mean Stakes Adjusted models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.80 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-11.15344 | Min. :-3.480000 | Min. :-829.4804 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 24.74 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.57965 | 1st Qu.:-0.040000 | 1st Qu.: -1.0939 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 29.22 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 40.53 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.02957 | Mean : 0.001888 | Mean : 0.0456 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 48.99 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.65576 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.3387 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :271.96 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 14.65678 | Max. : 3.040000 | Max. : 436.0988 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.3.3C : 41055 x 92 : Summary of Reversed rEMProbB weighted Kelly models year (mean value of stakes as staking adjuster) 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.3D : 19 x 5 : PL of Reversed rEMProbB weighted Kelly models (mean value of stakes as staking adjuster) year 2011~2015.
Median Fractional Models
Due to there has no league risk management profile, here I try to use the median value of stakes on every single league as the baseline.
Table 4.3.2.3E : Summary Table of Various Kelly Models (Reversed rEMProbB based with Mean Stakes Adjusted models)
| TimeUS | DateUS | Sess | League | Stakes | HCap | HKPrice | EUPrice | Result | Return | PL | PL.R | Rebates | RebatesS | rRates | netEMEdge | netProbB | rEMProbB | weight.stakes | weight | KStakesHKPriceEdge | KStakesnetProbBEdge | KStakesHKPrice | KStakesnetProbB | KStakesFixed | KStakesFixednetProbB | KStakesEMProb | KStakesEMProbnetProbB | KStakesHalf | KStakesHalfnetProbB | KStakesQuarter | KStakesQuarternetProbB | KStakesAdj | KStakesAdjnetProbB | KStakesHalfAdj | KStakesHalfAdjnetProbB | KStakesEMQuarterAdj | KStakesEMQuarterAdjnetProbB | KReturnHKPriceEdge | KReturnnetProbBEdge | KReturnHKPrice | KReturnnetProbB | KReturnFixed | KReturnFixednetProbB | KReturnEMProb | KReturnEMProbnetProbB | KReturnHalf | KReturnHalfnetProbB | KReturnQuarter | KReturnQuarternetProbB | KReturnAdj | KReturnAdjnetProbB | KReturnHalfAdj | KReturnHalfAdjnetProbB | KReturnEMQuarterAdj | KReturnEMQuarterAdjnetProbB | KPLHKPriceEdge | KPLnetProbBEdge | KPLHKPrice | KPLnetProbB | KPLFixed | KPLFixednetProbB | KPLEMProb | KPLEMProbnetProbB | KPLHalf | KPLHalfnetProbB | KPLQuarter | KPLQuarternetProbB | KPLAdj | KPLAdjnetProbB | KPLHalfAdj | KPLHalfAdjnetProbB | KPLEMQuarterAdj | KPLEMQuarterAdjnetProbB | KPLHKPriceEdge.R | KPLnetProbBEdge.R | KPLHKPrice.R | KPLnetProbB.R | KPLFixed.R | KPLFixednetProbB.R | KPLEMProb.R | KPLEMProbnetProbB.R | KPLHalf.R | KPLHalfnetProbB.R | KPLQuarter.R | KPLQuarternetProbB.R | KPLAdj.R | KPLAdjnetProbB.R | KPLHalfAdj.R | KPLHalfAdjnetProbB.R | KPLEMQuarterAdj.R | KPLEMQuarterAdjnetProbB.R | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Length:41055 | Min. :2011-01-07 | Min. :2011 | ENG PR : 1930 | Min. : 1.50 | Min. :-3.500 | Min. :0.1800 | Min. :1.180 | Cancelled: 28 | Min. : 0.00 | Min. :-1600.0000 | Min. :-23.18841 | Min. :-3.480000 | Min. :-488.0000 | Min. :1.005 | Min. :1.005 | Min. :0.0384 | Min. :0.03861 | Min. :1 | Min. :1 | Min. :0.00000 | Min. :0.0004317 | Min. :0.000000 | Min. :0.0002153 | Min. :0.002086 | Min. :0.0000261 | Min. :0.000000 | Min. :0.0002153 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.002086 | Min. :0.0000261 | Min. :2.218e-05 | Min. :2.000e-08 | Min. :2.360e-07 | Min. :0.000000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.00000 | Min. :0.000000 | Min. :0.000000 | Min. :-0.480983 | Min. :-0.295867 | Min. :-0.369870 | Min. :-0.14512 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.369870 | Min. :-0.14512 | Min. :0 | Min. :0 | Min. :0 | Min. :0 | Min. :-0.092192 | Min. :-0.123652 | Min. :-0.0226243 | Min. :-0.0471156 | Min. :-0.0064410 | Min. :-0.0193103 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.000 | Min. :-1.00000 | Min. : NA | Min. : NA | Min. : NA | Min. : NA | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | Min. :-1.00000 | |
| Class :character | 1st Qu.:2012-09-07 | 1st Qu.:2012 | FRA D2 : 1526 | 1st Qu.: 22.00 | 1st Qu.: 0.000 | 1st Qu.:0.7800 | 1st Qu.:1.780 | Half Loss: 2798 | 1st Qu.: 0.00 | 1st Qu.: -18.0000 | 1st Qu.: -0.67742 | 1st Qu.:-0.040000 | 1st Qu.: -0.9600 | 1st Qu.:1.006 | 1st Qu.:1.006 | 1st Qu.:0.4324 | 1st Qu.:0.44021 | 1st Qu.:1 | 1st Qu.:1 | 1st Qu.:0.00000 | 1st Qu.:0.0146583 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:0.000000 | 1st Qu.:0.0073057 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.078417 | 1st Qu.:0.0702398 | 1st Qu.:1.786e-02 | 1st Qu.:1.331e-02 | 1st Qu.:3.691e-03 | 1st Qu.:0.002459 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.00000 | 1st Qu.:0.000000 | 1st Qu.:0.000000 | 1st Qu.: 0.000000 | 1st Qu.:-0.020395 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.: 0.000000 | 1st Qu.:-0.01013 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:0 | 1st Qu.:-0.079189 | 1st Qu.:-0.079035 | 1st Qu.:-0.0189952 | 1st Qu.:-0.0179014 | 1st Qu.:-0.0041725 | 1st Qu.:-0.0043613 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.000 | 1st Qu.:-1.00000 | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.: NA | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | 1st Qu.:-1.00000 | |
| Mode :character | Median :2013-09-21 | Median :2013 | GER D1 : 1464 | Median : 26.00 | Median : 0.750 | Median :0.9300 | Median :1.930 | Half Win : 3052 | Median : 16.00 | Median : 0.0000 | Median : 0.00000 | Median : 0.000000 | Median : 0.0000 | Median :1.022 | Median :1.022 | Median :0.5105 | Median :0.51936 | Median :1 | Median :1 | Median :0.02525 | Median :0.0391126 | Median :0.001946 | Median :0.0193121 | Median :0.083649 | Median :0.0934369 | Median :0.001946 | Median :0.0193121 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.083649 | Median :0.0934369 | Median :2.027e-02 | Median :2.267e-02 | Median :4.905e-03 | Median :0.005569 | Median :0.00000 | Median :0.02200 | Median :0.00000 | Median :0.01096 | Median :0.08825 | Median :0.07878 | Median :0.00000 | Median :0.01096 | Median :0 | Median :0 | Median :0 | Median :0 | Median :0.08825 | Median :0.07878 | Median :0.02019 | Median :0.01472 | Median :0.004046 | Median :0.002717 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median : 0.000000 | Median : 0.000000 | Median : 0.000000 | Median : 0.00000 | Median :0 | Median :0 | Median :0 | Median :0 | Median : 0.000000 | Median : 0.000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.0000000 | Median : 0.365 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.365 | Median : 0.00000 | Median : NA | Median : NA | Median : NA | Median : NA | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | Median : 0.00000 | |
| NA | Mean :2013-08-05 | Mean :2013 | ITA D1 : 1412 | Mean : 33.26 | Mean : 1.075 | Mean :0.9443 | Mean :1.944 | Loss :14374 | Mean : 41.40 | Mean : 0.8713 | Mean : 0.03312 | Mean : 0.001888 | Mean : 0.0517 | Mean :1.022 | Mean :1.022 | Mean :0.5056 | Mean :0.51655 | Mean :1 | Mean :1 | Mean :0.06339 | Mean :0.0489270 | Mean :0.046313 | Mean :0.0240915 | Mean :0.081889 | Mean :0.0890077 | Mean :0.046313 | Mean :0.0240915 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.081889 | Mean :0.0890077 | Mean :1.913e-02 | Mean :2.326e-02 | Mean :4.584e-03 | Mean :0.006452 | Mean :0.06598 | Mean :0.05114 | Mean :0.04811 | Mean :0.02518 | Mean :0.08463 | Mean :0.09196 | Mean :0.04811 | Mean :0.02518 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean :0.08463 | Mean :0.09196 | Mean :0.01977 | Mean :0.02403 | Mean :0.004735 | Mean :0.006666 | Mean : 0.002589 | Mean : 0.002216 | Mean : 0.001798 | Mean : 0.00109 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.001798 | Mean : 0.00109 | Mean :0 | Mean :0 | Mean :0 | Mean :0 | Mean : 0.002744 | Mean : 0.002955 | Mean : 0.0006355 | Mean : 0.0007701 | Mean : 0.0001515 | Mean : 0.0002138 | Mean : 0.039 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.038 | Mean : 0.03322 | Mean :NaN | Mean :NaN | Mean :NaN | Mean :NaN | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | Mean : 0.03322 | |
| NA | 3rd Qu.:2014-09-18 | 3rd Qu.:2014 | SPA D1 : 1331 | 3rd Qu.: 36.00 | 3rd Qu.: 2.250 | 3rd Qu.:1.0800 | 3rd Qu.:2.080 | Push : 3778 | 3rd Qu.: 53.55 | 3rd Qu.: 20.3000 | 3rd Qu.: 0.76522 | 3rd Qu.: 0.040000 | 3rd Qu.: 1.1500 | 3rd Qu.:1.039 | 3rd Qu.:1.039 | 3rd Qu.:0.5851 | 3rd Qu.:0.59796 | 3rd Qu.:1 | 3rd Qu.:1 | 3rd Qu.:0.11136 | 3rd Qu.:0.0715989 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:0.083688 | 3rd Qu.:0.0354099 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.087022 | 3rd Qu.:0.1109033 | 3rd Qu.:2.116e-02 | 3rd Qu.:3.287e-02 | 3rd Qu.:5.642e-03 | 3rd Qu.:0.009738 | 3rd Qu.:0.10186 | 3rd Qu.:0.08923 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.06570 | 3rd Qu.:0.04399 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0.16013 | 3rd Qu.:0.16228 | 3rd Qu.:0.03631 | 3rd Qu.:0.03991 | 3rd Qu.:0.008549 | 3rd Qu.:0.010068 | 3rd Qu.: 0.026905 | 3rd Qu.: 0.036899 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.007840 | 3rd Qu.: 0.01818 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.:0 | 3rd Qu.: 0.075201 | 3rd Qu.: 0.072353 | 3rd Qu.: 0.0167193 | 3rd Qu.: 0.0169103 | 3rd Qu.: 0.0037956 | 3rd Qu.: 0.0039238 | 3rd Qu.: 0.780 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.760 | 3rd Qu.: 0.85000 | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: NA | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | 3rd Qu.: 0.85000 | |
| NA | Max. :2015-07-19 | Max. :2015 | FRA D1 : 1256 | Max. :160.00 | Max. : 8.250 | Max. :3.9000 | Max. :4.890 | Win :17025 | Max. :2992.00 | Max. : 1392.0000 | Max. : 22.98286 | Max. : 3.040000 | Max. : 256.0000 | Max. :1.039 | Max. :1.039 | Max. :0.9053 | Max. :0.91018 | Max. :1 | Max. :1 | Max. :0.62382 | Max. :0.4283007 | Max. :0.480695 | Max. :0.2107827 | Max. :0.092192 | Max. :0.1236515 | Max. :0.480695 | Max. :0.2107827 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.092192 | Max. :0.1236515 | Max. :2.262e-02 | Max. :4.712e-02 | Max. :6.441e-03 | Max. :0.019310 | Max. :0.68636 | Max. :0.42830 | Max. :0.53387 | Max. :0.21078 | Max. :0.17813 | Max. :0.30842 | Max. :0.53387 | Max. :0.21078 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. :0.17813 | Max. :0.30842 | Max. :0.05031 | Max. :0.13038 | Max. :0.016451 | Max. :0.056280 | Max. : 0.206719 | Max. : 0.119497 | Max. : 0.160893 | Max. : 0.05861 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.160893 | Max. : 0.05861 | Max. :0 | Max. :0 | Max. :0 | Max. :0 | Max. : 0.095716 | Max. : 0.199640 | Max. : 0.0310275 | Max. : 0.0861803 | Max. : 0.0108628 | Max. : 0.0383806 | Max. : 1.040 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 0.990 | Max. : 2.65000 | Max. : NA | Max. : NA | Max. : NA | Max. : NA | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | Max. : 2.65000 | |
| NA | NA | NA | (Other):32136 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA’s :17482 | NA | NA’s :20033 | NA | NA | NA | NA’s :20033 | NA | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA’s :41055 | NA | NA | NA | NA | NA | NA |
table 4.3.3.3E : 41055 x 92 : Summary of Reversed rEMProbB weighted Kelly models year (median value of stakes as staking adjuster) year 2011~2015.
From above table summary, we can know the range of risk management applicable to various adjusted Kelly models. Now we try to compare the Profit & Loss from below table.
table 4.3.3.3F : 19 x 5 : PL of Reversed rEMProbB weighted Kelly models (median value of stakes as staking adjuster) year 2011~2015.
## sample, need to modify...
suppressMessages(library('tidyverse'))
## weight function to get the likelihood staking amount, maximum likelihood methos will be applicable in section 4.5 and 4.6
#'@ n <- length(levels(dat$Result)) * nrow(dat)
#'@ mtx <- matrix(rep(0, n), nc = length(levels(dat$Result)), dimnames = list(NULL, levels(dat$Result))) %>% as.data.frame %>% tbl_df
#'@ mtx %<>% mutate(`Win` = ifelse(dat$Result == 'Win', 1, 0), `Half Win` = ifelse(dat$Result == 'Half Win', 1, 0), Push = ifelse(dat$Result == 'Half Loss', 1, 0), `Half Loss` = ifelse(dat$Result == 'Half Loss', 1, 0))
mtx <- dat %>% spread(Result, Stakes, fill = 0)
weight <- lm(Return ~ Win + `Half Win` + Push + `Half Loss` + Loss, data = mtx[c('Return', 'Stakes', 'Win', 'Half Win', 'Push', 'Half Loss', 'Loss')])
Bank Roll
suppressMessages(library('htmltools'))
ddply(K, .(Result), summarise, KReturn = sum(KReturn), Return = sum(Return), EUPrice = mean(EUPrice), HKPrice = mean(HKPrice), KStakes = sum(KStakes), Stakes = sum(Stakes), Rebates = sum(Rebates), Change = mean(Change)) %>% mutate(Stakes = currency(Stakes)) %>% tbl_df %>% formattable %>% as.htmlwidget
## Draft the further modelling
- Summarise the return
- measure the edge of odds price for staking
+ ln(Edge) = ln(Stakes) - ln(HKPrice) , Stakes/HKPrice
+ ln(Stakes) - ln(EUPrice) = (ln(Stakes) - ln(HKPrice)) - ((ln(Stakes) - ln(HKPrice)) + Stakes)
- generalize Kelly model
- Added the weight function
- simulate with different result and score
- Application of Maximum likelihood, Resampling and iteration to get the optimal weight value
- Simulate to compare the result or investment
## 1. Summarise the data which group by Date
accBets <- ddply(dat, .(Date), summarise, Stakes = sum(Stakes), S.median = median(Stakes), S.mean = mean(Stakes), S.sd = sd(Stakes), Count = length(PL), PL = sum(PL), PL.percent = PL / Stakes)
## 2. Set initial bankroll as 1,000,000
dat$iniBR <- c(1000000, cumsum(dat$Return[-1]))
dat$K <- ((dat$EUPrice + 1) * dat$rEMProbB - 1) / (dat$EUPrice)
exp(mean(log(dat$Stakes)))
## [1] 23.65785
There has few points we need to consider, there the we need to retrieve the initial investment capital \(BR\):
Table 4.3.2 : Summary data of daily bank roll (HKD$0’000)
| DateUS | Stakes | Return | PL | n | rRates | CumStakes | SPL | BR | gRates | gRates2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Min. :2011-01-07 | Min. : 4 | Min. : 0.0 | Min. :-2527.41 | Min. : 1.00 | Min. :0.0000 | Min. : 40 | Min. :-4587 | Min. : 13.05 | Min. : 0.04059 | Min. :0.002861 | |
| 1st Qu.:2012-04-01 | 1st Qu.: 328 | 1st Qu.: 293.5 | 1st Qu.: -126.69 | 1st Qu.: 9.00 | 1st Qu.:0.8128 | 1st Qu.: 384506 | 1st Qu.:10615 | 1st Qu.:15215.39 | 1st Qu.: 0.99420 | 1st Qu.:3.336709 | |
| Median :2013-06-04 | Median : 759 | Median : 773.2 | Median : 14.39 | Median : 19.00 | Median :1.0240 | Median : 827028 | Median :19262 | Median :23862.28 | Median : 1.00069 | Median :5.232957 | |
| Mean :2013-05-13 | Mean :1155 | Mean :1179.4 | Mean : 24.82 | Mean : 28.49 | Mean :1.0341 | Mean : 815158 | Mean :17774 | Mean :22373.80 | Mean : 1.08448 | Mean :4.906535 | |
| 3rd Qu.:2014-06-29 | 3rd Qu.:1520 | 3rd Qu.:1584.4 | 3rd Qu.: 182.97 | 3rd Qu.: 38.00 | 3rd Qu.:1.2596 | 3rd Qu.:1209336 | 3rd Qu.:24086 | 3rd Qu.:28686.30 | 3rd Qu.: 1.00895 | 3rd Qu.:6.290856 | |
| Max. :2015-07-19 | Max. :6108 | Max. :6613.1 | Max. : 3005.05 | Max. :148.00 | Max. :2.2033 | Max. :1663757 | Max. :38113 | Max. :42712.54 | Max. :117.42802 | Max. :9.366785 |
table 4.3.1.2 : 1441 x 11 : Sample data of daily bank roll.
Due to our bank roll cannot be less than 0, otherwie will be ruined. Therefore I added the initial balance of the account from the min value of variable SPL which is the balance before place bets must be more than 0. Otherwise unable to place bets.
From above table summary, we know that the gap of daily growth rate (variable gRates is geometric growth rates while gRates2 is initial fund baseline growth rates) is very big which is from 0.0405917 to 117.4280239 although the median value is 1.0006851. From initial paste0('HKD\$', r BR$BR[1] * 10000) lost to paste0('HKD\$', r min(BR$BR) * 10000) while the maximum bankroll hit paste0('HKD\$', r max(BR$BR) * 10000) which was 9.3667847 and the final bankroll is 8.9346861 times initial invested fund. The34 As I mentioned at the begining of the research paper, the stakes only reflects the profit and loss of agency A but not firm A. Firm A might have deal with 10~50 or even more agencies and the data from year 2011 is not the initial investment year. You are feel free to download the BankRoll.csv. We will discuss the inventory management to reduce the risk. From BankRoll.csv we observe the end of soccer sesson in May 2011 dat %>% filter(DateUS >= '2011-05-14' & DateUS <= '2011-05-21') has a seriourly crash. We can investigate more details about the loss matches from the data (or filter the range of the bets in the data table inside Part I).
Data has been collected over the last four seasons in the English Premier League. These include 1997-1998, 1998-1999, 1999-2000 and 2000-2001 seasons. We have also collected the season 2000-2001 data from the main European football betting leagues, such as English Division 1, Division 2 Division 3, Italian Serie A, German Bundesliga and Spanish Primera Liga…
quote 4.4.1 : the dataset for the studies (source : Niko Marttinen (2001)).
Niko Marttinen (2001)35 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. has enhanced the Dixon and Coles (1996) which are :
From above models, the author has compare the efficiency and the best fit model for scores prediction as below.
figure 4.4.1 : Comparison of various Poison models (source : Niko Marttinen (2001)).
From figure 4.4.1 above, the author compare the deviance of the models36 Kindly refer to Generalized Linear Models in R, Part 2: Understanding Model Fit in Logistic Regression Output, devianceTest and Use of Deviance Statistics for Comparing Models to learn about the method of comparison.
figure 4.4.2 : Comparison of various mixed Poison models II (source : Niko Marttinen (2001)).
figure 4.4.3 : Comparison of various mixed Poison models III (source : Niko Marttinen (2001)).
From above models, the author list the models and states that even though pick the worst model among the models still more accurate than bookmaker while E(Score)&Dep&Weighted is the best.
figure 4.4.4 : Comparison of various odds modelling models (source : Niko Marttinen (2001)).
Besides, Niko Marttinen (2001) not only choose Poison model throughly as the odds modelling model but also compare to below models :-
He concludes that the multinomial ordered probit model is the best fit model but the software for fitting is not generally available. Meanwhile, the Poisson model is more versatile than probit logit model based on the dataset accross the European soccer leagues.37 There has a lot of papers with regard to application of logit probit models on soccer betting, might read through and made comparison with my ®Model ®γσ, Eng Lian Hu (2016). I used to read though the logit probit and there has a complicated parameters setting for various effects like : wheather, players’ condition, couch, pitch condition and even though the distance travel and the players’ stamina modelling.
Here we introduce the Dixon and Coles (1996) model and its codes. You are freely learning from below links if interest.
table 4.4.1 : Samples of filtered multiple bets placed on same matches.
Due to the soccer matches randomly getting from different leagues, and also not Bernoulli win-lose result but half win-lose etc as we see from above. Besides, there were mixed Pre-Games and also In-Play soccer matches and I filter-up the sample data to be 16917 x 66. I don’t pretend to know the correct answer or the model from firm A. However I take a sample presentation Robert Johnson (2011)38 Kindly refer to 23th paper in 7.4 References from one of consultancy firm which is Dixon-Coles model and omitted the scoring process section.
Below is my previous research paper which was more sophiscated than Dixon-Coles model. You can refer it and I will just omit the section as mentioned at the beginning section of this staking validation research paper.
Here I cannot reverse computing from barely \(\rho_i^{EM}\) without know the \(\lambda_{ij}\) and \(\gamma\) values. Therefore I try to using both Home and Away Scores to simulate and test to get the maximum likelihood \(\rho_i^{EM}\).
\[X_{ij} = pois(\gamma \alpha_{ij} \beta_{ij} ); Y_{ij} = pois(\alpha_{ij} \beta_{ij}) \cdots equation\ 4.4.1\]
## model bivariate poison to retrieve the scores and resampling to get the likelihood value.
#'@ bvp()
In order to minimzie the risk, I tried to validate the odds price range invested by firm A.39 As I used to work in AS3388 which always take bets from Starlizard where they only placed bets within the odds price range from 0.70 ~ -0.70. They are not placed bets on all odds price in same edge. The sportbook consulatancy firms will not place same amount of stakes on same edge, lets take example as below :-
We know above edge is same but due to the probability of occurance an event/goal at 0.4 is smaller than 0.64. Here I try to bootstrap/resampling the scores of matches of the dataset and apply maximum likelihood on the poisson model to test the Kelly model and get the mean/likelihood value. Boostrapping the scores and staking model will be falling in the following sections [4.5 Staking Ⓜodel and Ⓜoney Management] and 4.6 Expectation Ⓜaximization and Staking Simulation.
From the article 凯利模式资金管理40 You might refer to Application of Kelly Criterion model in Sportsbook Investment as well. we know the application of generalization of Kelly criterion for uneven payoff games.
\[G: = \mathop {\lim }\limits_{N \to \infty } \frac{1}{N}\log\left( {\frac{{{S_N}}}{{{S_0}}}} \right) \cdots equation\ 4.3.2\]
In order to get the optimal value, I apply the bootrapping and resampling method.
\[L(\rho) = \prod_{i=1}^{n} (x_{i}|\rho) \cdots equation\ 4.3.4\]
Now we look at abpve function from a different perspective by considering the observed values \(x_{1}, x_{2}, x_{3}… x_{n}\) to be fixed parameters of this function, whereas \(\rho\) will be the function’s variable and allowed to vary freely; this function will be called the likelihood.
Below top-up and refill the fund into the pool is another method for risk management on money management while there is very dangerous if that leverage is higher. Similar with high leverage with contra in option market, endless pupm-in the fund will be very dangerous. Therefore we need to simulate what if the initial fund is smaller than the .
equation 4.3.3 : Economic Order Quantity (EOQ)
Base on above euqation, there has some criteria as below :
You are feel free to know about inventory management via Module 3: Inventory and Supply Chain Management.
C = Q/2 + 305958.2/Q
= Q^2 / 2Q + 611916.4 / 2Q
2QC = Q^2 + 611916.4
= Q^2 - 2QC + 611916.4 = 0
Q(Q - 2C) = 611916.4
Section : reverse modelling to get the EMProb prior to calculate the coefficient of the staking model. Otherwise might rearrange the order of applied Poison model here by refer to international competitions.
Galema, Plantinga and Scholtens (2008)41 You are feel free to refer to Reference for industry knowdelege and academic research portion for the paper. in 7.4 References for further details
draft :
- http://www.moneychimp.com/articles/risk/regression.htm
- read *Galema, Plantinga and Scholtens (2008)* https://englianhu.files.wordpress.com/2016/06/the-stocks-at-stake-return-and-risk-in-socially-responsible-investment.pdf
- reverse engineering on staking-profit linear regression model to get/retrieve EMProb value since now only get the coefficients figire of EMProb. Although incompleted soccer teams... 2ndly, reversed poison model from EMProb might is not workable on one-sided competition, need to refer to some international competition as references for incompleted dataset.
Martin Spann and Bernd Skiera (2009)42 Kindly refer to 19th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References applied a basic probability sets on the draw games and also the portion of win and loss. The author simply measured the portion of the draw result with win/loss to get the edge to place a bet. However it made a loss on Italian operator Oddset due to the 25% high vigorish but profitable in 12%. Secondly, the bets placed on fixed odds but not Asian Handicap and also a fixed amount $100.
sample… Geometric Mean
Investment Portfolio
张丹 (2016)43 Kindly refer to 7th paper inside Reference for technical research on programming and coding portion for the paper. in 7.4 References for further details provides couple of r package for investment and analysis in financial market.
Application of Monte Carlo simulation.
- simulate the resampling the stakes by mean and median value 100 times.
- simulate the poisson models for soccer matches result 100 times to compare the soccer result 0-0, 1-0, 0-1, etc.
- simulate the poisson models for place bets on various Handicap 100 times to compare the 'Win', 'Win-Half', 'Push', 'Loss-Half' and 'Loss' result.
- simulate the dynamic fractional Kelly model with weight parameter, yearly base.
- simulate whole process until get the optimal value...
Chapter 4.2 Comparison of Different Feature Sets and Betting Strategies in
Dixon and Pope (2003) apply linear model to compare the efficiency of the odds prices offer by first three largest Firm A, B and C in UK.
By refer to ®γσ, Eng Lian Hu (2016)44 Kindly refer to 28th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References, here I apply the arules and arulesViz packages to analyse the market basket of the bets.
Due to the data-sets I collected just one among all agents among couple sports-bookmakers 4lowin. Here I cannot determine if the sample data among the population…
JA : What skills and academic training (example: college courses) are valuable to sports statisticians?
KW : I would say there are three sets of skills you need to be a successful sports statistician:
- Quantitative skills - the statistical and mathematical techniques you’ll use to make sense of the data. Most kinds of coursework you’d find in an applied statistics program will be helpful. Regression methods, hypothesis testing, confidence intervals, inference, probability, ANOVA, multivariate analysis, linear and logistic models, clustering, time series, and data mining/machine learning would all be applicable. I’d include in this category designing charts, graphs, and other data visualizations to help present and communicate results.
- Technical skills - learning one or more statistical software systems such as R/S-PLUS, SAS, SPSS, Stata, Matlab, etc. will give you the tools to apply quantitative skills in practice. Beyond that, the more self-reliant you are at extracting and manipulating your data directly, the more quickly you can explore your data and test ideas. So being adept with the technology you’re likely to encounter will help tremendously. Most of the information you’d be dealing with in sports statistics would be in a database, so learning SQL or another query language is important. In addition, mastering advanced spreadsheet skills such as pivot tables, macros, scripting, and chart customization would be useful.
- Domain knowledge - truly understanding the sport you want to analyze professionally is critical to being successful. Knowing the rules of the game; studying how front offices operate; finding out how players are recruited, developed, and evaluated; and even just learning the jargon used within the industry will help you integrate into the organization. You’ll come to understand what problems are important to the GM and other decisionmakers, as well as what information is available, how it’s collected, what it means, and what its limitations are. Also, I recommend keeping up with the discussions in your sport’s analytic community so you know about the latest developments and what’s considered the state of the art in the public sphere. One of the great things about being a sports statistician is getting to follow your favorite websites and blogs as a legitimate part of your job!
source : Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field
In this Part II research paper I try to add a section which is filtered out only English soccer leagues and the revenue and profit & loss all sessional based but not annum based to make it applicable to my future staking in real world. The proportional staking and also money management on the staking pools. You are feel free to browse from the content page Betting Strategy and Model Validation.
… … …
Niko Marttinen (2001) has conducted a very detail and useful but also applicable betting system in real life. There has a ordered probit model which shows a high accuracy predictive model compare to his Poisson (Escore) model. Well, the ®γσ, Lian Hu ENG (2016)45 The research modelling with testing the efficiency of odds price which had completed in year 2010. Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has build a weight inflated diagonal poisson model which is more complicated and shophitiscated and later ®γσ, Lian Hu ENG (2014)46 Kindly refer to 4th paper inside Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. However there has an automatically and systematically trading system which wrote in VBA + S-Plus + Excel + SQL47 the betting system has stated in his paper. which is very useful as reference. The author use VBA to automac the algorithmic trading while there has no Asian Handicap and Goal Line odds price data to simulate compare to mine. While currently the shinyapps with RStudioConnect can also build an algorithmic trading system. However the session timeout issue48 The connection timeout issue might be a big issue for real time algorithmic trading might need to consider. The shinydashboard example from ョStudio might probably cope with the issue.
John Fingleton & Patrick Waldron (1999) applied Shin model to test the portion of hedge funds and smart punters. As I stated in 4.2 Linear Ⓜodel, the sparkR, RHadoop and noSQL require in order to analyse the high volume betslips dataset. Its interesting and will conduct the research if all betslips of bookmaker(s) is(are) available in the future.
From the 4.3 Kelly Ⓜodel we test the staking model, the table 4.2.1 we apply the linear models and choose the best fit model based on the edge of odds price. 4.4 Poisson Ⓜodel we try to reverse the odds price placed to get the probabilities of scoring different scores. Now we try to test the return of staking on different handicap (ex: 0, 0.25, 0.5, 0.75, 1 etc.) to know which handicap earn the most. Nowadays the hotest matches of four major leagues provides few handicaps market, there will be another case study and research to increase the profit base on same probabilities and also edge but staking on different handicap. The dataset will be collect for research beyond the future.
I will be apply Shiny to write a dynamic website to utilise the function as web based apps. I am currently conducting another research on Analyse the Finance and Stocks Price of Bookmakers which is an analysis on the public listed companies and also anonymous companies revenue and profit & loss. You are welcome to refer SHOW ME SHINY and build your own shinyapps.
I will also write as a package to easier load and log.
If you get interest to be a punter, you are feel free to read over below presentation paper from a British consultancy firm to know the requirement to be a professional gambler.
It’s useful to record some information about how your file was created.
[1] “2016-10-31 21:21:30 JST”
Firstly I do appreciate those who shade me a light on my research. Meanwhile I do happy and learn from the research.
Due to the rmarkdown file has quite some sections and titles, you might expand or collapse the codes by refer to Code Folding and Sections for easier reading.
There are quite some errors when I knit HTML:
let say always stuck (which is not response and consider as completed) at 29%. I tried couple times while sometimes prompt me different errors (upgrade Droplet to larger RAM memory space doesn’t helps) and eventually apply rm() and gc() to remove the object after use and also clear the memory space.
Need to reload the package suppressAll(library('networkD3')) which in chunk decission-tree-A prior to apply function simpleNetwork while I load it in chunk libs at the beginning of the section 1. Otherwise cannot found that particlar function.
The rCharts::rPlot() works fine if run in chunk, but error when knit the rmarkdown file. Raised an issue : Error : rCharts::rPlot() in rmarkdown file.
xtable always shows LaTeX output but not table. Raised a question in COS : 求助!knitr Rmd pdf 中文编译 2016年8月19日 下午9:56 7 楼.Here I try other packages like textreg and stargazer. You can refer to Test version to view the output of stargazer function and the source codes I reserved but added eval = FALSE in chunks named lm-summary and lm-anova to unexecute the codes.
I refer to R Shiny: Rendering summary.ivreg output and tried to plot the output table, but there has no bottom statistical information like Residual standard error, Degree of Freedom, R-Squared, F-statistical value and also p-value, therefore I use R Shiny App for Linear Regression, Issue with Render Functions which simply renderPrint() the verbatimTextOutput() in shinyapp 4.2.1.
I tried to raise an issue about post the shinyapps to RStudioConnect at Unable publish to RStudio Connect : Error in yaml::yaml.load(enc2utf8(string), …) : Reader error: control characters are not allowed: #81 at 276 #115. You might try to refer to the gif files in #issue 115 for further information. I tried couple times and find the solution but there has no an effective solution and only allowed post to ョPubs.com where I finally decide to seperate the dynamic shinyApp into another web url.
Remark : When I rewrite Report with ShinyApps : Linear Regression Analysis on Odds Price of Stakes and would like to post to ®StudioConnect, the wizard only allowed me post to rPubs.com (but everyone know rPubs only allow static document which is not effort to support Shinyapp). Therefore kindly refer to https://beta.rstudioconnect.com/content/1766/. You might download and run locally due to web base version always affected by wizards and sometimes only view datatable but sometimes only can view googleVis while sometimes unable access.
Using formattable and plotly simultaneously and Possible namespace issue with plotly::last_plot() #41 solved the formattable issue.
The analysis in Part I might slightly different with Part II due to the timezone issue.
I am currently work as a customer service operator and self research as a smart punter. Hope my sportsbook hedge fund company website Scibrokes® running business soon…
Terminator II
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